Heat

In thermodynamics, heat is energy in transfer to or from a thermodynamic system, by mechanisms other than thermodynamic work or transfer of matter.[1][2][3][4][5][6][7] The mechanisms include conduction, through direct contact of immobile bodies, or through a wall or barrier that is impermeable to matter; or radiation between separated bodies; or isochoric mechanical work done by the surroundings on the system of interest; or Joule heating by an electric current driven through the system of interest by an external system; or a combination of these. When there is a suitable path between two systems with different temperatures, heat transfer occurs necessarily, immediately, and spontaneously from the hotter to the colder system. Thermal conduction occurs by the stochastic (random) motion of microscopic particles (such as atoms or molecules). In contrast, thermodynamic work is defined by mechanisms that act macroscopically and directly on the system's whole-body state variables; for example, change of the system's volume through a piston's motion with externally measurable force; or change of the system's internal electric polarization through an externally measurable change in electric field. The definition of heat transfer does not require that the process be in any sense smooth. For example, a bolt of lightning may transfer heat to a body.

Convective circulation allows one body to heat another, through an intermediate circulating fluid that carries energy from a boundary of one to a boundary of the other; the actual heat transfer is by conduction and radiation between the fluid and the respective bodies.[8][9][10] Natural convection, though spontaneous, does not occur merely because of temperature difference but due to Rayleigh instability caused by combination of gravity and thermal expansion in supplement to sufficient temperature gradient.

Like thermodynamic work, heat transfer is a process involving two systems, not a property of any one system. In thermodynamics, energy transferred as heat (a process function) contributes to change in the system's cardinal energy variable of state, for example its internal energy, or for example its enthalpy. This is to be distinguished from the ordinary language conception of heat as a property of the system.

Although heat flows spontaneously from a hotter body to a cooler one, it is possible to construct a heat pump which expends work to transfer energy from a colder body to a hotter body. In contrast, a heat engine reduces an existing temperature difference to supply work to another system. Another thermodynamic type of heat transfer device is an active heat spreader, which expends work to speed up transfer of energy to colder surroundings from a hotter body, for example a computer component.[11]

The amount of heat transferred in any process can be defined as the total amount of transferred energy excluding any macroscopic work that was done and any energy contained in matter transferred. For the precise definition of heat, it is necessary that it occur by a path that does not include transfer of matter.[12] As an amount of energy (being transferred), the SI unit of heat is the joule (J). The conventional symbol used to represent the amount of heat transferred in a thermodynamic process is Q. Heat is measured by its effect on the states of interacting bodies, for example, by the amount of ice melted or a change in temperature.[13] The quantification of heat via the temperature change of a body is called calorimetry.

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The Sun and Earth form an ongoing example of a heating process. Some of the Sun's thermal radiation strikes and heats the Earth. Compared to the Sun, Earth has a much lower temperature and so sends far less thermal radiation back to the Sun. The heat of this process can be quantified by the net amount, and direction (Sun to Earth), of energy it transferred in a given period of time.

Notation and units

As a form of energy, heat has the unit joule (J) in the International System of Units (SI). However, in many applied fields in engineering the British thermal unit (BTU) and the calorie are often used. The standard unit for the rate of heat transferred is the watt (W), defined as one joule per second.

Use of the symbol Q for the total amount of energy transferred as heat is due to Rudolf Clausius in 1850:

"Let the amount of heat which must be imparted during the transition of the gas in a definite manner from any given state to another, in which its volume is v and its temperature t, be called Q"[14]

Heat released by a system into its surroundings is by convention a negative quantity (Q < 0); when a system absorbs heat from its surroundings, it is positive (Q > 0). Heat transfer rate, or heat flow per unit time, is denoted by . This should not be confused with a time derivative of a function of state (which can also be written with the dot notation) since heat is not a function of state.[15] Heat flux is defined as rate of heat transfer per unit cross-sectional area (units watts per square metre).

Classical thermodynamics

Heat and entropy

Clausius-1
Rudolf Clausius

In 1856, Rudolf Clausius, referring to closed systems, in which transfers of matter do not occur, defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat Q from work at the temperature T, has the equivalence-value:"[16][17]

In 1865, he came to define the entropy symbolized by S, such that, due to the supply of the amount of heat Q at temperature T the entropy of the system is increased by

In a transfer of energy as heat without work being done, there are changes of entropy in both the surroundings which lose heat and the system which gains it. The increase, ΔS, of entropy in the system may be considered to consist of two parts, an increment, ΔS that matches, or 'compensates', the change, −ΔS, of entropy in the surroundings, and a further increment, ΔS′′ that may be considered to be 'generated' or 'produced' in the system, and is said therefore to be 'uncompensated'. Thus

This may also be written

The total change of entropy in the system and surroundings is thus

This may also be written

It is then said that an amount of entropy ΔS has been transferred from the surroundings to the system. Because entropy is not a conserved quantity, this is an exception to the general way of speaking, in which an amount transferred is of a conserved quantity.

From the second law of thermodynamics follows that in a spontaneous transfer of heat, in which the temperature of the system is different from that of the surroundings:

For purposes of mathematical analysis of transfers, one thinks of fictive processes that are called reversible, with the temperature T of the system being hardly less than that of the surroundings, and the transfer taking place at an imperceptibly slow rate.

Following the definition above in formula (1), for such a fictive reversible process, a quantity of transferred heat δQ (an inexact differential) is analyzed as a quantity T dS, with dS (an exact differential):

This equality is only valid for a fictive transfer in which there is no production of entropy, that is to say, in which there is no uncompensated entropy.

If, in contrast, the process is natural, and can really occur, with irreversibility, then there is entropy production, with dSuncompensated > 0. The quantity T dSuncompensated was termed by Clausius the "uncompensated heat", though that does not accord with present-day terminology. Then one has

This leads to the statement

which is the second law of thermodynamics for closed systems.

In non-equilibrium thermodynamics that approximates by assuming the hypothesis of local thermodynamic equilibrium, there is a special notation for this. The transfer of energy as heat is assumed to take place across an infinitesimal temperature difference, so that the system element and its surroundings have near enough the same temperature T. Then one writes

where by definition

The second law for a natural process asserts that

[18][19][20][21]

Heat and enthalpy

For a closed system (a system from which no matter can enter or exit), one version of the first law of thermodynamics states that the change in internal energy ΔU of the system is equal to the amount of heat Q supplied to the system minus the amount of work W done by system on its surroundings. The foregoing sign convention for work is used in the present article, but an alternate sign convention, followed by IUPAC, for work, is to consider the work performed on the system by its surroundings as positive. This is the convention adopted by many modern textbooks of physical chemistry, such as those by Peter Atkins and Ira Levine, but many textbooks on physics define work as work done by the system.

This formula can be re-written so as to express a definition of quantity of energy transferred as heat, based purely on the concept of adiabatic work, if it is supposed that ΔU is defined and measured solely by processes of adiabatic work:

The work done by the system includes boundary work (when the system increases its volume against an external force, such as that exerted by a piston) and other work (e.g. shaft work performed by a compressor fan), which is called isochoric work:

In this Section we will neglect the "other-" or isochoric work contribution.

The internal energy, U, is a state function. In cyclical processes, such as the operation of a heat engine, state functions of the working substance return to their initial values upon completion of a cycle.

The differential, or infinitesimal increment, for the internal energy in an infinitesimal process is an exact differential dU. The symbol for exact differentials is the lowercase letter d.

In contrast, neither of the infinitesimal increments δQ nor δW in an infinitesimal process represents the state of the system. Thus, infinitesimal increments of heat and work are inexact differentials. The lowercase Greek letter delta, δ, is the symbol for inexact differentials. The integral of any inexact differential over the time it takes for a system to leave and return to the same thermodynamic state does not necessarily equal zero.

As recounted below, in the section headed Entropy, the second law of thermodynamics observes that if heat is supplied to a system in which no irreversible processes take place and which has a well-defined temperature T, the increment of heat δQ and the temperature T form the exact differential

and that S, the entropy of the working body, is a function of state. Likewise, with a well-defined pressure, P, behind the moving boundary, the work differential, δW, and the pressure, P, combine to form the exact differential

with V the volume of the system, which is a state variable. In general, for homogeneous systems,

Associated with this differential equation is that the internal energy may be considered to be a function U (S,V) of its natural variables S and V. The internal energy representation of the fundamental thermodynamic relation is written

[22][23]

If V is constant

and if P is constant

with H the enthalpy defined by

The enthalpy may be considered to be a function H (S,P) of its natural variables S and P. The enthalpy representation of the fundamental thermodynamic relation is written

[23][24]

The internal energy representation and the enthalpy representation are partial Legendre transforms of one another. They contain the same physical information, written in different ways. Like the internal energy, the enthalpy stated as a function of its natural variables is a thermodynamic potential and contains all thermodynamic information about a body.[24][25]

If a quantity Q of heat is added to a body while it does expansion work W on its surroundings, one has

If this is constrained to happen at constant pressure with ΔP = 0, the expansion work W done by the body is given by W = P ΔV; recalling the first law of thermodynamics, one has

Consequently, by substitution one has

In this scenario, the increase in enthalpy is equal to the quantity of heat added to the system. Since many processes do take place at constant pressure, or approximately at atmospheric pressure, the enthalpy is therefore sometimes given the misleading name of 'heat content'.[26] It is sometimes also called the heat function.[27]

In terms of the natural variables S and P of the state function H, this process of change of state from state 1 to state 2 can be expressed as

It is known that the temperature T(S, P) is identically stated by

Consequently,

In this case, the integral specifies a quantity of heat transferred at constant pressure.

History

As a common noun, English heat or warmth (just as French chaleur, German Wärme, Latin calor, Greek θάλπος, etc.) refers to (the human perception of) either thermal energy or temperature. Speculation on thermal energy or "heat" as a separate form of matter has a long history, see caloric theory, phlogiston and fire (classical element).

The modern understanding of thermal energy originates with Thompson's 1798 mechanical theory of heat (An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction), postulating a mechanical equivalent of heat. A collaboration between Nicolas Clément and Sadi Carnot (Reflections on the Motive Power of Fire) in the 1820s had some related thinking near the same lines.[28] In 1845, Joule published a paper entitled The Mechanical Equivalent of Heat, in which he specified a numerical value for the amount of mechanical work required to "produce a unit of heat". The theory of classical thermodynamics matured in the 1850s to 1860s. John Tyndall's Heat Considered as Mode of Motion (1863) was instrumental in popularising the idea of heat as motion to the English-speaking public. The theory was developed in academic publications in French, English and German. From an early time, the French technical term chaleur used by Carnot was taken as equivalent to the English heat and German Wärme (lit. "warmth", the equivalent of heat would be German Hitze).

The process function Q was introduced by Rudolf Clausius in 1850. Clausius described it with the German compound Wärmemenge, translated as "amount of heat".[14]

James Clerk Maxwell in his 1871 Theory of Heat outlines four stipulations for the definition of heat:

  • It is something which may be transferred from one body to another, according to the second law of thermodynamics.
  • It is a measurable quantity, and so can be treated mathematically.
  • It cannot be treated as a material substance, because it may be transformed into something that is not a material substance, e.g., mechanical work.
  • Heat is one of the forms of energy.[29]

The process function Q is referred to as Wärmemenge by Clausius, or as "amount of heat" in translation. Use of "heat" as an abbreviated form of the specific concept of "quantity of energy transferred as heat" led to some terminological confusion by the early 20th century. The generic meaning of "heat", even in classical thermodynamics, is just "thermal energy".[30] Since the 1920s, it has been recommended practice to use enthalpy to refer to the "heat content at constant volume", and to thermal energy when "heat" in the general sense is intended, while "heat" is reserved for the very specific context of the transfer of thermal energy between two systems. Leonard Benedict Loeb in his Kinetic Theory of Gases (1927) makes a point of using "quanitity of heat" or "heat–quantity" when referring to Q:[31]

After the perfection of thermometry [...] the next great advance made in the field of heat was the definition of a term which is called the quantity of heat. [... after the abandonment of caloric theory,] It still remains to interpret this very definite concept, the quantity of heat, in terms of a theory ascribing all heat to the kinetics of gas molecules.

[32]

Carathéodory (1909)

A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system.[33][34][35][36][37][38]

The internal energy UX of a body in an arbitrary state X can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state O. Such work is assessed through quantities defined in the surroundings of the body. It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition. The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter. In particular they do not allow the passage of energy as heat. According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body. On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, diathermal walls, which are postulated to be permeable only to heat.

For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest Y is reached from state O by a process with two components, one adiabatic and the other not adiabatic. For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work. Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body. The change in internal energy to reach the state Y from the state O is the difference of the two amounts of energy transferred.

Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, Q, to the body from its surroundings, in the combined process of change to state Y from the state O, as the change in internal energy, ΔUY, minus the amount of work, W, done by the body on its surrounds by the adiabatic process, so that Q = ΔUYW.

In this definition, for the sake of conceptual rigour, the quantity of energy transferred as heat is not specified directly in terms of the non-adiabatic process. It is defined through knowledge of precisely two variables, the change of internal energy and the amount of adiabatic work done, for the combined process of change from the reference state O to the arbitrary state Y. It is important that this does not explicitly involve the amount of energy transferred in the non-adiabatic component of the combined process. It is assumed here that the amount of energy required to pass from state O to state Y, the change of internal energy, is known, independently of the combined process, by a determination through a purely adiabatic process, like that for the determination of the internal energy of state X above. The rigour that is prized in this definition is that there is one and only one kind of energy transfer admitted as fundamental: energy transferred as work. Energy transfer as heat is considered as a derived quantity. The uniqueness of work in this scheme is considered to guarantee rigor and purity of conception. The conceptual purity of this definition, based on the concept of energy transferred as work as an ideal notion, relies on the idea that some frictionless and otherwise non-dissipative processes of energy transfer can be realized in physical actuality. The second law of thermodynamics, on the other hand, assures us that such processes are not found in nature.

Before the rigorous mathematical definition of heat based on Carathéodory's 1909 paper, historically, heat, temperature, and thermal equilibrium were presented in thermodynamics textbooks as jointly primitive notions.[39] Carathéodory introduced his 1909 paper thus: "The proposition that the discipline of thermodynamics can be justified without recourse to any hypothesis that cannot be verified experimentally must be regarded as one of the most noteworthy results of the research in thermodynamics that was accomplished during the last century." Referring to the "point of view adopted by most authors who were active in the last fifty years", Carathéodory wrote: "There exists a physical quantity called heat that is not identical with the mechanical quantities (mass, force, pressure, etc.) and whose variations can be determined by calorimetric measurements." James Serrin introduces an account of the theory of thermodynamics thus: "In the following section, we shall use the classical notions of heat, work, and hotness as primitive elements, ... That heat is an appropriate and natural primitive for thermodynamics was already accepted by Carnot. Its continued validity as a primitive element of thermodynamical structure is due to the fact that it synthesizes an essential physical concept, as well as to its successful use in recent work to unify different constitutive theories."[40][41] This traditional kind of presentation of the basis of thermodynamics includes ideas that may be summarized by the statement that heat transfer is purely due to spatial non-uniformity of temperature, and is by conduction and radiation, from hotter to colder bodies. It is sometimes proposed that this traditional kind of presentation necessarily rests on "circular reasoning"; against this proposal, there stands the rigorously logical mathematical development of the theory presented by Truesdell and Bharatha (1977).[42]

This alternative approach to the definition of quantity of energy transferred as heat differs in logical structure from that of Carathéodory, recounted just above.

This alternative approach admits calorimetry as a primary or direct way to measure quantity of energy transferred as heat. It relies on temperature as one of its primitive concepts, and used in calorimetry.[43] It is presupposed that enough processes exist physically to allow measurement of differences in internal energies. Such processes are not restricted to adiabatic transfers of energy as work. They include calorimetry, which is the commonest practical way of finding internal energy differences.[44] The needed temperature can be either empirical or absolute thermodynamic.

In contrast, the Carathéodory way recounted just above does not use calorimetry or temperature in its primary definition of quantity of energy transferred as heat. The Carathéodory way regards calorimetry only as a secondary or indirect way of measuring quantity of energy transferred as heat. As recounted in more detail just above, the Carathéodory way regards quantity of energy transferred as heat in a process as primarily or directly defined as a residual quantity. It is calculated from the difference of the internal energies of the initial and final states of the system, and from the actual work done by the system during the process. That internal energy difference is supposed to have been measured in advance through processes of purely adiabatic transfer of energy as work, processes that take the system between the initial and final states. By the Carathéodory way it is presupposed as known from experiment that there actually physically exist enough such adiabatic processes, so that there need be no recourse to calorimetry for measurement of quantity of energy transferred as heat. This presupposition is essential but is explicitly labeled neither as a law of thermodynamics nor as an axiom of the Carathéodory way. In fact, the actual physical existence of such adiabatic processes is indeed mostly supposition, and those supposed processes have in most cases not been actually verified empirically to exist.[45]

Heat transfer

Heat transfer between two bodies

Referring to conduction, Partington writes: "If a hot body is brought in conducting contact with a cold body, the temperature of the hot body falls and that of the cold body rises, and it is said that a quantity of heat has passed from the hot body to the cold body."[46]

Referring to radiation, Maxwell writes: "In Radiation, the hotter body loses heat, and the colder body receives heat by means of a process occurring in some intervening medium which does not itself thereby become hot."[47]

Maxwell writes that convection as such "is not a purely thermal phenomenon".[48] In thermodynamics, convection in general is regarded as transport of internal energy. If, however, the convection is enclosed and circulatory, then it may be regarded as an intermediary that transfers energy as heat between source and destination bodies, because it transfers only energy and not matter from the source to the destination body.[10]

In accordance with the first law for closed systems, energy transferred solely as heat leaves one body and enters another, changing the internal energies of each. Transfer, between bodies, of energy as work is a complementary way of changing internal energies. Though it is not logically rigorous from the viewpoint of strict physical concepts, a common form of words that expresses this is to say that heat and work are interconvertible.

Cyclically operating engines, that use only heat and work transfers, have two thermal reservoirs, a hot and a cold one. They may be classified by the range of operating temperatures of the working body, relative to those reservoirs. In a heat engine, the working body is at all times colder than the hot reservoir and hotter than the cold reservoir. In a sense, it uses heat transfer to produce work. In a heat pump, the working body, at stages of the cycle, goes both hotter than the hot reservoir, and colder than the cold reservoir. In a sense, it uses work to produce heat transfer.

Heat engine

In classical thermodynamics, a commonly considered model is the heat engine. It consists of four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A cyclic process leaves the working body in an unchanged state, and is envisaged as being repeated indefinitely often. Work transfers between the working body and the work reservoir are envisaged as reversible, and thus only one work reservoir is needed. But two thermal reservoirs are needed, because transfer of energy as heat is irreversible. A single cycle sees energy taken by the working body from the hot reservoir and sent to the two other reservoirs, the work reservoir and the cold reservoir. The hot reservoir always and only supplies energy and the cold reservoir always and only receives energy. The second law of thermodynamics requires that no cycle can occur in which no energy is received by the cold reservoir. Heat engines achieve higher efficiency when the difference between initial and final temperature is greater.

Heat pump or refrigerator

Another commonly considered model is the heat pump or refrigerator. Again there are four bodies: the working body, the hot reservoir, the cold reservoir, and the work reservoir. A single cycle starts with the working body colder than the cold reservoir, and then energy is taken in as heat by the working body from the cold reservoir. Then the work reservoir does work on the working body, adding more to its internal energy, making it hotter than the hot reservoir. The hot working body passes heat to the hot reservoir, but still remains hotter than the cold reservoir. Then, by allowing it to expand without doing work on another body and without passing heat to another body, the working body is made colder than the cold reservoir. It can now accept heat transfer from the cold reservoir to start another cycle.

The device has transported energy from a colder to a hotter reservoir, but this is not regarded as by an inanimate agency; rather, it is regarded as by the harnessing of work . This is because work is supplied from the work reservoir, not just by a simple thermodynamic process, but by a cycle of thermodynamic operations and processes, which may be regarded as directed by an animate or harnessing agency. Accordingly, the cycle is still in accord with the second law of thermodynamics. The efficiency of a heat pump is best when the temperature difference between the hot and cold reservoirs is least.

Functionally, such engines are used in two ways, distinguishing a target reservoir and a resource or surrounding reservoir. A heat pump transfers heat, to the hot reservoir as the target, from the resource or surrounding reservoir. A refrigerator transfers heat, from the cold reservoir as the target, to the resource or surrounding reservoir. The target reservoir may be regarded as leaking: when the target leaks hotness to the surroundings, heat pumping is used; when the target leaks coldness to the surroundings, refrigeration is used. The engines harness work to overcome the leaks.

Macroscopic view

According to Planck, there are three main conceptual approaches to heat.[49] One is the microscopic or kinetic theory approach. The other two are macroscopic approaches. One is the approach through the law of conservation of energy taken as prior to thermodynamics, with a mechanical analysis of processes, for example in the work of Helmholtz. This mechanical view is taken in this article as currently customary for thermodynamic theory. The other macroscopic approach is the thermodynamic one, which admits heat as a primitive concept, which contributes, by scientific induction[50] to knowledge of the law of conservation of energy. This view is widely taken as the practical one, quantity of heat being measured by calorimetry.

Bailyn also distinguishes the two macroscopic approaches as the mechanical and the thermodynamic.[51] The thermodynamic view was taken by the founders of thermodynamics in the nineteenth century. It regards quantity of energy transferred as heat as a primitive concept coherent with a primitive concept of temperature, measured primarily by calorimetry. A calorimeter is a body in the surroundings of the system, with its own temperature and internal energy; when it is connected to the system by a path for heat transfer, changes in it measure heat transfer. The mechanical view was pioneered by Helmholtz and developed and used in the twentieth century, largely through the influence of Max Born.[52] It regards quantity of heat transferred as heat as a derived concept, defined for closed systems as quantity of heat transferred by mechanisms other than work transfer, the latter being regarded as primitive for thermodynamics, defined by macroscopic mechanics. According to Born, the transfer of internal energy between open systems that accompanies transfer of matter "cannot be reduced to mechanics".[53] It follows that there is no well-founded definition of quantities of energy transferred as heat or as work associated with transfer of matter.

Nevertheless, for the thermodynamical description of non-equilibrium processes, it is desired to consider the effect of a temperature gradient established by the surroundings across the system of interest when there is no physical barrier or wall between system and surroundings, that is to say, when they are open with respect to one another. The impossibility of a mechanical definition in terms of work for this circumstance does not alter the physical fact that a temperature gradient causes a diffusive flux of internal energy, a process that, in the thermodynamic view, might be proposed as a candidate concept for transfer of energy as heat.

In this circumstance, it may be expected that there may also be active other drivers of diffusive flux of internal energy, such as gradient of chemical potential which drives transfer of matter, and gradient of electric potential which drives electric current and iontophoresis; such effects usually interact with diffusive flux of internal energy driven by temperature gradient, and such interactions are known as cross-effects.[54]

If cross-effects that result in diffusive transfer of internal energy were also labeled as heat transfers, they would sometimes violate the rule that pure heat transfer occurs only down a temperature gradient, never up one. They would also contradict the principle that all heat transfer is of one and the same kind, a principle founded on the idea of heat conduction between closed systems. One might to try to think narrowly of heat flux driven purely by temperature gradient as a conceptual component of diffusive internal energy flux, in the thermodynamic view, the concept resting specifically on careful calculations based on detailed knowledge of the processes and being indirectly assessed. In these circumstances, if perchance it happens that no transfer of matter is actualized, and there are no cross-effects, then the thermodynamic concept and the mechanical concept coincide, as if one were dealing with closed systems. But when there is transfer of matter, the exact laws by which temperature gradient drives diffusive flux of internal energy, rather than being exactly knowable, mostly need to be assumed, and in many cases are practically unverifiable. Consequently, when there is transfer of matter, the calculation of the pure 'heat flux' component of the diffusive flux of internal energy rests on practically unverifiable assumptions.[55][quotations 1][56] This is a reason to think of heat as a specialized concept that relates primarily and precisely to closed systems, and applicable only in a very restricted way to open systems.

In many writings in this context, the term "heat flux" is used when what is meant is therefore more accurately called diffusive flux of internal energy; such usage of the term "heat flux" is a residue of older and now obsolete language usage that allowed that a body may have a "heat content".[57]

Microscopic view

In the kinetic theory, heat is explained in terms of the microscopic motions and interactions of constituent particles, such as electrons, atoms, and molecules.[58] The immediate meaning of the kinetic energy of the constituent particles is not as heat. It is as a component of internal energy. In microscopic terms, heat is a transfer quantity, and is described by a transport theory, not as steadily localized kinetic energy of particles. Heat transfer arises from temperature gradients or differences, through the diffuse exchange of microscopic kinetic and potential particle energy, by particle collisions and other interactions. An early and vague expression of this was made by Francis Bacon.[59][60] Precise and detailed versions of it were developed in the nineteenth century.[61]

In statistical mechanics, for a closed system (no transfer of matter), heat is the energy transfer associated with a disordered, microscopic action on the system, associated with jumps in occupation numbers of the energy levels of the system, without change in the values of the energy levels themselves.[62] It is possible for macroscopic thermodynamic work to alter the occupation numbers without change in the values of the system energy levels themselves, but what distinguishes transfer as heat is that the transfer is entirely due to disordered, microscopic action, including radiative transfer. A mathematical definition can be formulated for small increments of quasi-static adiabatic work in terms of the statistical distribution of an ensemble of microstates.

Calorimetry

Quantity of heat transferred can be measured by calorimetry, or determined through calculations based on other quantities.

Calorimetry is the empirical basis of the idea of quantity of heat transferred in a process. The transferred heat is measured by changes in a body of known properties, for example, temperature rise, change in volume or length, or phase change, such as melting of ice.[63][64]

A calculation of quantity of heat transferred can rely on a hypothetical quantity of energy transferred as adiabatic work and on the first law of thermodynamics. Such calculation is the primary approach of many theoretical studies of quantity of heat transferred.[33][65][66]

Engineering

Hot metalwork
A red-hot iron rod from which heat transfer to the surrounding environment will be primarily through radiation.

The discipline of heat transfer, typically considered an aspect of mechanical engineering and chemical engineering, deals with specific applied methods by which thermal energy in a system is generated, or converted, or transferred to another system. Although the definition of heat implicitly means the transfer of energy, the term heat transfer encompasses this traditional usage in many engineering disciplines and laymen language.

Heat transfer is generally described as including the mechanisms of heat conduction, heat convection, thermal radiation, but may include mass transfer and heat in processes of phase changes.

Convection may be described as the combined effects of conduction and fluid flow. From the thermodynamic point of view, heat flows into a fluid by diffusion to increase its energy, the fluid then transfers (advects) this increased internal energy (not heat) from one location to another, and this is then followed by a second thermal interaction which transfers heat to a second body or system, again by diffusion. This entire process is often regarded as an additional mechanism of heat transfer, although technically, "heat transfer" and thus heating and cooling occurs only on either end of such a conductive flow, but not as a result of flow. Thus, conduction can be said to "transfer" heat only as a net result of the process, but may not do so at every time within the complicated convective process.

Latent and sensible heat

Black Joseph
Joseph Black

In an 1847 lecture entitled On Matter, Living Force, and Heat, James Prescott Joule characterized the terms latent heat and sensible heat as components of heat each affecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.[67][quotations 2] He described latent energy as the energy possessed via a distancing of particles where attraction was over a greater distance, i.e. a form of potential energy, and the sensible heat as an energy involving the motion of particles, i.e. kinetic energy.

Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a change of state that occurs without a change in temperature. Such a process may be a phase transition, such as the melting of ice or the boiling of water.[68][69]

Heat capacity

Heat capacity is a measurable physical quantity equal to the ratio of the heat added to an object to the resulting temperature change.[70] The molar heat capacity is the heat capacity per unit amount (SI unit: mole) of a pure substance, and the specific heat capacity, often called simply specific heat, is the heat capacity per unit mass of a material. Heat capacity is a physical property of a substance, which means that it depends on the state and properties of the substance under consideration.

The specific heats of monatomic gases, such as helium, are nearly constant with temperature. Diatomic gases such as hydrogen display some temperature dependence, and triatomic gases (e.g., carbon dioxide) still more.

Before the development of the laws of thermodynamics, heat was measured by changes in the states of the participating bodies.

Some general rules, with important exceptions, can be stated as follows.

In general, most bodies expand on heating. In this circumstance, heating a body at a constant volume increases the pressure it exerts on its constraining walls, while heating at a constant pressure increases its volume.

Beyond this, most substances have three ordinarily recognized states of matter, solid, liquid, and gas. Some can also exist in a plasma. Many have further, more finely differentiated, states of matter, such as for example, glass, and liquid crystal. In many cases, at fixed temperature and pressure, a substance can exist in several distinct states of matter in what might be viewed as the same 'body'. For example, ice may float in a glass of water. Then the ice and the water are said to constitute two phases within the 'body'. Definite rules are known, telling how distinct phases may coexist in a 'body'. Mostly, at a fixed pressure, there is a definite temperature at which heating causes a solid to melt or evaporate, and a definite temperature at which heating causes a liquid to evaporate. In such cases, cooling has the reverse effects.

All of these, the commonest cases, fit with a rule that heating can be measured by changes of state of a body. Such cases supply what are called thermometric bodies, that allow the definition of empirical temperatures. Before 1848, all temperatures were defined in this way. There was thus a tight link, apparently logically determined, between heat and temperature, though they were recognized as conceptually thoroughly distinct, especially by Joseph Black in the later eighteenth century.

There are important exceptions. They break the obviously apparent link between heat and temperature. They make it clear that empirical definitions of temperature are contingent on the peculiar properties of particular thermometric substances, and are thus precluded from the title 'absolute'. For example, water contracts on being heated near 277 K. It cannot be used as a thermometric substance near that temperature. Also, over a certain temperature range, ice contracts on heating. Moreover, many substances can exist in metastable states, such as with negative pressure, that survive only transiently and in very special conditions. Such facts, sometimes called 'anomalous', are some of the reasons for the thermodynamic definition of absolute temperature.

In the early days of measurement of high temperatures, another factor was important, and used by Josiah Wedgwood in his pyrometer. The temperature reached in a process was estimated by the shrinkage of a sample of clay. The higher the temperature, the more the shrinkage. This was the only available more or less reliable method of measurement of temperatures above 1000 °C. But such shrinkage is irreversible. The clay does not expand again on cooling. That is why it could be used for the measurement. But only once. It is not a thermometric material in the usual sense of the word.

Nevertheless, the thermodynamic definition of absolute temperature does make essential use of the concept of heat, with proper circumspection.

"Hotness"

According to Denbigh (1981), the property of hotness is a concern of thermodynamics that should be defined without reference to the concept of heat. Consideration of hotness leads to the concept of empirical temperature.[71] All physical systems are capable of heating or cooling others.[72] With reference to hotness, the comparative terms hotter and colder are defined by the rule that heat flows from the hotter body to the colder.[73][74][75]

If a physical system is inhomogeneous or very rapidly or irregularly changing, for example by turbulence, it may be impossible to characterize it by a temperature, but still there can be transfer of energy as heat between it and another system. If a system has a physical state that is regular enough, and persists long enough to allow it to reach thermal equilibrium with a specified thermometer, then it has a temperature according to that thermometer. An empirical thermometer registers degree of hotness for such a system. Such a temperature is called empirical.[76][77][78] For example, Truesdell writes about classical thermodynamics: "At each time, the body is assigned a real number called the temperature. This number is a measure of how hot the body is."[79]

Physical systems that are too turbulent to have temperatures may still differ in hotness. A physical system that passes heat to another physical system is said to be the hotter of the two. More is required for the system to have a thermodynamic temperature. Its behavior must be so regular that its empirical temperature is the same for all suitably calibrated and scaled thermometers, and then its hotness is said to lie on the one-dimensional hotness manifold. This is part of the reason why heat is defined following Carathéodory and Born, solely as occurring other than by work or transfer of matter; temperature is advisedly and deliberately not mentioned in this now widely accepted definition.

This is also the reason that the zeroth law of thermodynamics is stated explicitly. If three physical systems, A, B, and C are each not in their own states of internal thermodynamic equilibrium, it is possible that, with suitable physical connections being made between them, A can heat B and B can heat C and C can heat A. In non-equilibrium situations, cycles of flow are possible. It is the special and uniquely distinguishing characteristic of internal thermodynamic equilibrium that this possibility is not open to thermodynamic systems (as distinguished amongst physical systems) which are in their own states of internal thermodynamic equilibrium; this is the reason why the zeroth law of thermodynamics needs explicit statement. That is to say, the relation 'is not colder than' between general non-equilibrium physical systems is not transitive, whereas, in contrast, the relation 'has no lower a temperature than' between thermodynamic systems in their own states of internal thermodynamic equilibrium is transitive. It follows from this that the relation 'is in thermal equilibrium with' is transitive, which is one way of stating the zeroth law.

Just as temperature may be undefined for a sufficiently inhomogeneous system, so also may entropy be undefined for a system not in its own state of internal thermodynamic equilibrium. For example, 'the temperature of the solar system' is not a defined quantity. Likewise, 'the entropy of the solar system' is not defined in classical thermodynamics. It has not been possible to define non-equilibrium entropy, as a simple number for a whole system, in a clearly satisfactory way.[80]

See also

References

  1. ^ Reif (1965): "[in the special case of purely thermal interaction between two system:] The mean energy transferred from one system to the other as a result of purely thermal interaction is called 'heat'" (p. 67). the quantity Q [...] is simply a measure of the mean energy change not due to the change of external parameters. [...] splits the total mean energy change into a part W due to mechanical interaction and a part Q due to thermal interaction [...] by virtue of [the definition ΔU = QW, present notation, physics sign convention], both heat and work have the dimensions of energy" (p. 73). C.f.: "heat is thermal energy in transfer" Stephen J. Blundell, Katherine M. Blundell, Concepts in Thermal Physics (2009), p. 13 Archived 24 June 2018 at the Wayback Machine.
  2. ^ Thermodynamics and an Introduction to Thermostatics, 2nd Edition, by Herbert B. Callen, 1985, http://cvika.grimoar.cz/callen/ Archived 17 October 2018 at the Wayback Machine or http://keszei.chem.elte.hu/1alapFizkem/H.B.Callen-Thermodynamics.pdf Archived 30 December 2016 at the Wayback Machine , p. 8: Energy may be transferred via ... work. "But it is equally possible to transfer energy via the hidden atomic modes of motion as well as via those that happen to be macroscopically observable. An energy transfer via the hidden atomic modes is called heat."
  3. ^ Born, M. (1949), p. 31.
  4. ^ Pippard, A.B. (1957/1966), p. 16.
  5. ^ Landau, L., Lifshitz, E.M. (1958/1969), p. 43
  6. ^ Callen, H.B. (1960/1985), pp. 18–19.
  7. ^ Bailyn, M. (1994), p. 82.
  8. ^ Guggenheim, E.A. (1949/1967), p. 8
  9. ^ Planck. M. (1914)
  10. ^ a b Chandrasekhar, S. (1961).
  11. ^ Adams, M.J.,Verosky, M., Zebarjadi, M., Heremans, J.P. (2019). Active Peltier Coolers Based on Correlated and Magnon-Drag Metals, Phys. Rev. Applied11, 054008 (2019)
  12. ^ >Born, M. (1949), p. 44.
  13. ^ Maxwell, J.C. (1871), Chapter III.
  14. ^ a b Die Wärmemenge, welche dem Gase mitgetheilt werden muss, während es aus irgend einem früheren Zustande auf einem bestimmten Wege in den Zustand übergeführt wird, in welchem sein Volumen = v und seine Temperatur = t ist, möge Q heissen R. Clausius, Ueber die bewegende Kraft der Wärme und die Gesetze, welche sich daraus für die Wärmelehre selbst ableiten lassen Archived 17 April 2019 at the Wayback Machine, communication to the Academy of Berlin, February 1850, published in Pogendorff's Annalen vol. 79, March/April 1850, first translated in Philosophical Magazine vol. 2, July 1851, as "First Memoir" in: The Mechanical Theory of Heat, with its Applications to the Steam-Engine and to the Physical Properties of Bodies, trans. John Tyndall, London, 1867, p. 25.
  15. ^ Baierlein, R. (1999), p. 21.
  16. ^ Clausius, R. (1854).
  17. ^ Clausius, R. (1865), pp. 125–126.
  18. ^ De Groot, S.R., Mazur, P. (1962), p. 20.
  19. ^ Kondepudi, D, Prigogine, I. (1998), p. 82.
  20. ^ Kondepudi, D. (2008), p. 114.
  21. ^ Lebon, g., Jou, D., Casas-Vásquez, J. (2008), p. 41.
  22. ^ Callen, H.B., (1985), Section 2-3, pp. 40–42.
  23. ^ a b Adkins, C.J. (1983), p. 101.
  24. ^ a b Callen, H.B. (1985), p. 147.
  25. ^ Adkins, C.J. (1983), pp. 100–104.
  26. ^ Adkins, C.J. (1968/1983), p. 46.
  27. ^ Bailyn, M. (1994), p. 208.
  28. ^ Lervig, P. Sadi Carnot and the steam engine:Nicolas Clément's lectures on industrial chemistry, 1823–28. Br. J Hist. Sci. 18:147, 1985.
  29. ^ Maxwell, J.C. (1871), p. 7.
  30. ^ "in a gas, heat is nothing else than the kinetic or mechanical energy of motion of the gas molecules". B.L. Loeb, The Kinetic Theory of Gases (1927), p. 14.
  31. ^ From this terminological choice may derive a tradition to the effect that the letter Q represents "quantity", but there is no indication that Clausius had this in mind when he selected the letter in what seemed to be an ad hoc calculation in 1850.
  32. ^ B.L. Loeb, The Kinetic Theory of Gases (1927), p. 426 Archived 24 June 2018 at the Wayback Machine.
  33. ^ a b Carathéodory, C. (1909).
  34. ^ Adkins, C.J. (1968/1983).
  35. ^ Münster, A. (1970).
  36. ^ Pippard, A.B. (1957).
  37. ^ Fowler, R., Guggenheim, E.A. (1939).
  38. ^ Buchdahl, H.A. (1966).
  39. ^ Lieb, E.H., Yngvason, J. (1999), p. 10.
  40. ^ Serrin, J. (1986), p. 5.
  41. ^ Owen, D.R. (1984), pp. 43–45.
  42. ^ Truesdell, C., Bharatha, S. (1977).
  43. ^ Maxwell, J.C. (1871), p.v.
  44. ^ Atkins, P., de Paula, J. (1978/2010), p. 54.
  45. ^ Pippard, A.B. (1957/1966), p. 15.
  46. ^ Partington, J.R. (1949), p. 118.
  47. ^ Maxwell, J.C. (1871), p. 10.
  48. ^ Maxwell, J.C. (1871), p. 11.
  49. ^ Planck, M. (1897/1903), p. viii.
  50. ^ Hintikka, J. (1988), p. 180.
  51. ^ Bailyn, M. (1994), pp. 65, 79.
  52. ^ Born, M.(1949), Lecture V.
  53. ^ Born, M. (1949), p. 44.
  54. ^ De Groot, S.R., Mazur, P. (1962), p. 30.
  55. ^ Denbigh, K.G. (1951), p. 56.
  56. ^ Fitts, D.D. (1962), p. 28.
  57. ^ Gyarmati, I. (1970), p. 68.
  58. ^ Kittel, C. Kroemer, H. (1980).
  59. ^ Bacon, F. (1620).
  60. ^ Partington, J.R. (1949), p. 131.
  61. ^ Partington, J.R. (1949), pp. 132–136.
  62. ^ Reif (1965), pp. 67–68
  63. ^ Maxwell J.C. (1872), p. 54.
  64. ^ Planck (1927), Chapter 3.
  65. ^ Bryan, G.H. (1907), p. 47.
  66. ^ Callen, H.B. (1985), Section 1-8.
  67. ^ Joule J.P. (1884).
  68. ^ Perrot, P. (1998).
  69. ^ Clark, J.O.E. (2004).
  70. ^ Halliday, David; Resnick, Robert (2013). Fundamentals of Physics. Wiley. p. 524.
  71. ^ Denbigh, K. (1981), p. 9.
  72. ^ Baierlein, R. (1999), p. 349.
  73. ^ Adkins, C.J. (1968/1983), p. 34.
  74. ^ Pippard, A.B. (1957/1966), p. 18.
  75. ^ Haase, R. (1971), p. 7.
  76. ^ Mach, E. (1900), section 5, pp. 48–49, section 22, pp. 60–61.
  77. ^ Truesdell, C. (1980).
  78. ^ Serrin, J. (1986), especially p. 6.
  79. ^ Truesdell, C. (1969), p. 6.
  80. ^ Lieb, E.H., Yngvason, J. (2003), p. 190.

Quotations

  1. ^ Denbigh states in a footnote that he is indebted to correspondence with Professor E.A. Guggenheim and with Professor N.K. Adam. From this, Denbigh concludes "It seems, however, that when a system is able to exchange both heat and matter with its environment, it is impossible to make an unambiguous distinction between energy transported as heat and by the migration of matter, without already assuming the existence of the 'heat of transport'." Denbigh K.G. (1951), p. 56.
  2. ^ "Heat must therefore consist of either living force or of attraction through space. In the former case we can conceive the constituent particles of heated bodies to be, either in whole or in part, in a state of motion. In the latter we may suppose the particles to be removed by the process of heating, so as to exert attraction through greater space. I am inclined to believe that both of these hypotheses will be found to hold good,—that in some instances, particularly in the case of sensible heat, or such as is indicated by the thermometer, heat will be found to consist in the living force of the particles of the bodies in which it is induced; whilst in others, particularly in the case of latent heat, the phenomena are produced by the separation of particle from particle, so as to cause them to attract one another through a greater space." Joule, J.P. (1884).

Bibliography of cited references

  • Adkins, C.J. (1968/1983). Equilibrium Thermodynamics, (1st edition 1968), third edition 1983, Cambridge University Press, Cambridge UK, ISBN 0-521-25445-0.
  • Atkins, P., de Paula, J. (1978/2010). Physical Chemistry, (first edition 1978), ninth edition 2010, Oxford University Press, Oxford UK, ISBN 978-0-19-954337-3.
  • Bacon, F. (1620). Novum Organum Scientiarum, translated by Devey, J., P.F. Collier & Son, New York, 1902.
  • Baierlein, R. (1999). Thermal Physics. Cambridge University Press. ISBN 978-0-521-65838-6.
  • Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3.
  • Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London.
  • Bryan, G.H. (1907). Thermodynamics. An Introductory Treatise dealing mainly with First Principles and their Direct Applications, B.G. Teubner, Leipzig.
  • Buchdahl, H.A. (1966). The Concepts of Classical Thermodynamics, Cambridge University Press, Cambridge UK.
  • Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, (1st edition 1960) 2nd edition 1985, Wiley, New York, ISBN 0-471-86256-8.
  • Carathéodory, C. (1909). "Untersuchungen über die Grundlagen der Thermodynamik" (PDF). Mathematische Annalen. 67 (3): 355–386. doi:10.1007/BF01450409. A translation may be found here. A mostly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA.
  • Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford UK.
  • Clark, J.O.E. (2004). The Essential Dictionary of Science. Barnes & Noble Books. ISBN 978-0-7607-4616-5.
  • Clausius, R. (1854). Annalen der Physik (Poggendoff's Annalen), Dec. 1854, vol. xciii. p. 481; translated in the Journal de Mathematiques, vol. xx. Paris, 1855, and in the Philosophical Magazine, August 1856, s. 4. vol. xii, p. 81.
  • Clausius, R. (1865/1867). The Mechanical Theory of Heat – with its Applications to the Steam Engine and to Physical Properties of Bodies, London: John van Voorst. 1867. Also the second edition translated into English by W.R. Browne (1879) here and here.
  • De Groot, S.R., Mazur, P. (1962). Non-equilibrium Thermodynamics, North-Holland, Amsterdam. Reprinted (1984), Dover Publications Inc., New York, ISBN 0486647412.
  • Denbigh, K. (1955/1981). The Principles of Chemical Equilibrium, Cambridge University Press, Cambridge ISBN 0-521-23682-7.
  • Greven, A., Keller, G., Warnecke (editors) (2003). Entropy, Princeton University Press, Princeton NJ, ISBN 0-691-11338-6.
  • Guggenheim, E.A. (1967) [1949], Thermodynamics. An Advanced Treatment for Chemists and Physicists (fifth ed.), Amsterdam: North-Holland Publishing Company.
  • Jensen, W.B. (2010). "Why Are q and Q Used to Symbolize Heat?" (PDF). J. Chem. Educ. 87 (11): 1142. Bibcode:2010JChEd..87.1142J. doi:10.1021/ed100769d. Archived from the original (PDF) on 2 April 2015. Retrieved 23 March 2015.
  • J.P. Joule (1884), The Scientific Papers of James Prescott Joule, The Physical Society of London, p. 274, Lecture on Matter, Living Force, and Heat. 5 and 12 May 1847.
  • Kittel, C. Kroemer, H. (1980). Thermal Physics, second edition, W.H. Freeman, San Francisco, ISBN 0-7167-1088-9.
  • Kondepudi, D. (2008), Introduction to Modern Thermodynamics, Chichester UK: Wiley, ISBN 978-0-470-01598-8
  • Kondepudi, D., Prigogine, I. (1998). Modern Thermodynamics: From Heat Engines to Dissipative Structures, John Wiley & Sons, Chichester, ISBN 0-471-97393-9.
  • Landau, L., Lifshitz, E.M. (1958/1969). Statistical Physics, volume 5 of Course of Theoretical Physics, translated from the Russian by J.B. Sykes, M.J. Kearsley, Pergamon, Oxford.
  • Lebon, G., Jou, D., Casas-Vázquez, J. (2008). Understanding Non-equilibrium Thermodynamics: Foundations, Applications, Frontiers, Springer-Verlag, Berlin, e-ISBN 978-3-540-74252-4.
  • Lieb, E.H., Yngvason, J. (2003). The Entropy of Classical Thermodynamics, Chapter 8 of Entropy, Greven, A., Keller, G., Warnecke (editors) (2003).
  • Maxwell, J.C. (1871), Theory of Heat (first ed.), London: Longmans, Green and Co.
  • Partington, J.R. (1949), An Advanced Treatise on Physical Chemistry., 1, Fundamental Principles. The Properties of Gases, London: Longmans, Green and Co.
  • Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 978-0-19-856552-9.
  • Pippard, A.B. (1957/1966). Elements of Classical Thermodynamics for Advanced Students of Physics, original publication 1957, reprint 1966, Cambridge University Press, Cambridge.
  • Planck, M., (1897/1903). Treatise on Thermodynamics, translated by A. Ogg, first English edition, Longmans, Green and Co., London.
  • Planck. M. (1914). The Theory of Heat Radiation, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.
  • Planck, M., (1923/1927). Treatise on Thermodynamics, translated by A. Ogg, third English edition, Longmans, Green and Co., London.
  • Reif, F. (1965). Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hlll, Inc.
  • Shavit, A., Gutfinger, C. (1995). Thermodynamics. From Concepts to Applications, Prentice Hall, London, ISBN 0-13-288267-1.
  • Truesdell, C. (1969). Rational Thermodynamics: a Course of Lectures on Selected Topics, McGraw-Hill Book Company, New York.
  • Truesdell, C. (1980). The Tragicomical History of Thermodynamics 1822–1854, Springer, New York, ISBN 0-387-90403-4.

Further bibliography

  • Beretta, G.P.; E.P. Gyftopoulos (1990). "What is heat?" (PDF). Education in Thermodynamics and Energy Systems. AES. 20.
  • Gyftopoulos, E.P., & Beretta, G.P. (1991). Thermodynamics: foundations and applications. (Dover Publications)
  • Hatsopoulos, G.N., & Keenan, J.H. (1981). Principles of general thermodynamics. RE Krieger Publishing Company.

External links

Air conditioning

Air conditioning (often referred to as AC, A/C, or air con) is the process of removing heat and moisture from the interior of an occupied space to improve the comfort of occupants. Air conditioning can be used in both domestic and commercial environments. This process is most commonly used to achieve a more comfortable interior environment, typically for humans and other animals; however, air conditioning is also used to cool and dehumidify rooms filled with heat-producing electronic devices, such as computer servers, power amplifiers, and to display and store some delicate products, such as artwork.

Air conditioners often use a fan to distribute the conditioned air to an occupied space such as a building or a car to improve thermal comfort and indoor air quality. Electric refrigerant-based AC units range from small units that can cool a small bedroom, which can be carried by a single adult, to massive units installed on the roof of office towers that can cool an entire building. The cooling is typically achieved through a refrigeration cycle, but sometimes evaporation or free cooling is used. Air conditioning systems can also be made based on desiccants (chemicals which remove moisture from the air). Some AC systems reject or store heat in subterranean pipes.In construction, a complete system of heating, ventilation, and air conditioning is referred to as HVAC.

Convection

Convection is the heat transfer due to the bulk movement of molecules within fluids such as gases and liquids, including molten rock (rheid). Convection includes sub-mechanisms of advection (directional bulk-flow transfer of heat), and diffusion (non-directional transfer of energy or mass particles along a concentration gradient).

Convection cannot take place in most solids because neither bulk current flows nor significant diffusion of matter can take place. Diffusion of heat takes place in rigid solids, but that is called heat conduction. Convection, additionally may take place in soft solids or mixtures where solid particles can move past each other.

Thermal convection can be demonstrated by placing a heat source (e.g. a Bunsen burner) at the side of a glass filled with a liquid, and observing the changes in temperature in the glass caused by the warmer fluid circulating into cooler areas.

Convective heat transfer is one of the major types of heat transfer, and convection is also a major mode of mass transfer in fluids. Convective heat and mass transfer takes place both by diffusion – the random Brownian motion of individual particles in the fluid – and by advection, in which matter or heat is transported by the larger-scale motion of currents in the fluid. In the context of heat and mass transfer, the term "convection" is used to refer to the combined effects of advective and diffusive transfer. Sometimes the term "convection" is used to refer specifically to "free heat convection" (natural heat convection) where bulk-flow in a fluid is due to temperature-induced differences in buoyancy, as opposed to "forced heat convection" where forces other than buoyancy (such as pump or fan) move the fluid. However, in mechanics, the correct use of the word "convection" is the more general sense, and different types of convection should be further qualified, for clarity.

Convection can be qualified in terms of being natural, forced, gravitational, granular, or thermomagnetic. It may also be said to be due to combustion, capillary action, or Marangoni and Weissenberg effects. Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its mantle. Discrete convective cells in the atmosphere can be seen as clouds, with stronger convection resulting in thunderstorms. Natural convection also plays a role in stellar physics.

The convection mechanism is also used in cooking, when using a convection oven, which uses fans to circulate hot air around food in order to cook the food faster than a conventional oven.

Dwyane Wade

Dwyane Tyrone Wade Jr. ( dwayn; born January 17, 1982) is an American former professional basketball player. Wade spent the majority of his 16-year career playing for the Miami Heat in the National Basketball Association (NBA). After a successful college basketball career with the Marquette Golden Eagles, Wade was drafted fifth overall in the 2003 NBA draft by the Heat. In his third season, Wade led the Heat to their first NBA Championship in franchise history and was named the 2006 NBA Finals MVP. At the 2008 Summer Olympics, Wade led the United States men's basketball team, commonly known as the "Redeem Team", in scoring and helped them capture the gold medal. In the 2008–09 season, Wade led the league in scoring and earned his first NBA scoring title. With LeBron James and Chris Bosh, Wade helped guide Miami to four consecutive NBA Finals from 2011 to 2014, winning back-to-back championships in 2012 and 2013. After playing for the Chicago Bulls and the Cleveland Cavaliers, Wade was traded back to Miami in February 2018. A 13-time NBA All-Star, Wade is Miami's all-time leader in points, games, assists, and steals, shots made and shots taken.

Energy

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of 1 metre against a force of 1 newton.

Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.

Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.

Living organisms require energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth.

Engine

An engine or motor is a machine designed to convert one form of energy into mechanical energy. Heat engines, like the internal combustion engine, burn a fuel to create heat which is then used to do work. Electric motors convert electrical energy into mechanical motion, pneumatic motors use compressed air, and clockwork motors in wind-up toys use elastic energy. In biological systems, molecular motors, like myosins in muscles, use chemical energy to create forces and eventually motion.

Entropy

In statistical mechanics, entropy is an extensive property of a thermodynamic system. It is closely related to the number Ω of microscopic configurations (known as microstates) that are consistent with the macroscopic quantities that characterize the system (such as its volume, pressure and temperature). Entropy expresses the number Ω of different configurations that a system defined by macroscopic variables could assume. Under the assumption that each microstate is equally probable, the entropy is the natural logarithm of the number of microstates, multiplied by the Boltzmann constant kB. Formally (assuming equiprobable microstates),

Macroscopic systems typically have a very large number Ω of possible microscopic configurations. For example, the entropy of an ideal gas is proportional to the number of gas molecules N. The number of molecules in twenty liters of gas at room temperature and atmospheric pressure is roughly N6×1023 (the Avogadro number).

The second law of thermodynamics states that the entropy of an isolated system never decreases over time. Isolated systems spontaneously evolve towards thermodynamic equilibrium, the state with maximum entropy. Non-isolated systems, like organisms, may lose entropy, provided their environment's entropy increases by at least that amount so that the total entropy increases. Therefore, total entropy in the Universe does increase. Entropy is a function of the state of the system, so the change in entropy of a system is determined by its initial and final states. In the idealization that a process is reversible, the entropy does not change, while irreversible processes always increase the total entropy.

Because it is determined by the number of random microstates, entropy is related to the amount of additional information needed to specify the exact physical state of a system, given its macroscopic specification. For this reason, it is often said that entropy is an expression of the disorder, or randomness of a system, or of the lack of information about it. The concept of entropy plays a central role in information theory.

Heat capacity

Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to a given mass of a material to produce a unit change in its temperature.The SI unit of heat capacity is joule per kelvin (J/K).

Heat capacity is an extensive property. The corresponding intensive property is the specific heat capacity. Dividing the heat capacity by the amount of substance in moles yields its molar heat capacity. The volumetric heat capacity measures the heat capacity per volume.

Heat capacity is often said as thermal mass in architecture and civil engineering to refer to the heat capacity of a building .

Heat exchanger

A heat exchanger is a system used to transfer heat between two or more fluids. Heat exchangers are used in both cooling and heating processes. The fluids may be separated by a solid wall to prevent mixing or they may be in direct contact. They are widely used in space heating, refrigeration, air conditioning, power stations, chemical plants, petrochemical plants, petroleum refineries, natural-gas processing, and sewage treatment. The classic example of a heat exchanger is found in an internal combustion engine in which a circulating fluid known as engine coolant flows through radiator coils and air flows past the coils, which cools the coolant and heats the incoming air. Another example is the heat sink, which is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant.

Heat transfer

Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. Engineers also consider the transfer of mass of differing chemical species, either cold or hot, to achieve heat transfer. While these mechanisms have distinct characteristics, they often occur simultaneously in the same system.

Heat conduction, also called diffusion, is the direct microscopic exchange of kinetic energy of particles through the boundary between two systems. When an object is at a different temperature from another body or its surroundings, heat flows so that the body and the surroundings reach the same temperature, at which point they are in thermal equilibrium. Such spontaneous heat transfer always occurs from a region of high temperature to another region of lower temperature, as described in the second law of thermodynamics.

Heat convection occurs when bulk flow of a fluid (gas or liquid) carries heat along with the flow of matter in the fluid. The flow of fluid may be forced by external processes, or sometimes (in gravitational fields) by buoyancy forces caused when thermal energy expands the fluid (for example in a fire plume), thus influencing its own transfer. The latter process is often called "natural convection". All convective processes also move heat partly by diffusion, as well. Another form of convection is forced convection. In this case the fluid is forced to flow by use of a pump, fan or other mechanical means.

Thermal radiation occurs through a vacuum or any transparent medium (solid or fluid or gas). It is the transfer of energy by means of photons in electromagnetic waves governed by the same laws.

Heating, ventilation, and air conditioning

Heating, ventilation, and air conditioning (HVAC) is the technology of indoor and vehicular environmental comfort. Its goal is to provide thermal comfort and acceptable indoor air quality. HVAC system design is a subdiscipline of mechanical engineering, based on the principles of thermodynamics, fluid mechanics and heat transfer. "Refrigeration" is sometimes added to the field's abbreviation, as HVAC&R or HVACR or "ventilation" is dropped, as in HACR (as in the designation of HACR-rated circuit breakers).

HVAC is an important part of residential structures such as single family homes, apartment buildings, hotels and senior living facilities, medium to large industrial and office buildings such as skyscrapers and hospitals, vehicles such as cars, trains, airplanes, ships and submarines, and in marine environments, where safe and healthy building conditions are regulated with respect to temperature and humidity, using fresh air from outdoors.

Ventilating or ventilation (the V in HVAC) is the process of exchanging or replacing air in any space to provide high indoor air quality which involves temperature control, oxygen replenishment, and removal of moisture, odors, smoke, heat, dust, airborne bacteria, carbon dioxide, and other gases. Ventilation removes unpleasant smells and excessive moisture, introduces outside air, keeps interior building air circulating, and prevents stagnation of the interior air.

Ventilation includes both the exchange of air to the outside as well as circulation of air within the building. It is one of the most important factors for maintaining acceptable indoor air quality in buildings. Methods for ventilating a building may be divided into mechanical/forced and natural types.

Joule

The joule (/dʒaʊl, dʒuːl/ jawl, jool; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one metre (1 newton metre or N⋅m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

In terms firstly of base SI units and then in terms of other SI units, a joule is defined below, where kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt:

One joule can also be defined as the following:

The joule is named after James Prescott Joule. As with every SI unit named for a person, its symbol starts with an upper case letter (J), but when written in full it follows the rules for capitalisation of a common noun; i.e., "joule" becomes capitalised at the beginning of a sentence and in titles, but is otherwise in lower case.

LeBron James

LeBron Raymone James Sr. (; born December 30, 1984) is an American professional basketball player for the Los Angeles Lakers of the National Basketball Association (NBA). He is often regarded as the greatest basketball player of all time. His accomplishments include three NBA championships, four NBA Most Valuable Player Awards, three NBA Finals MVP Awards, and two Olympic gold medals. James has appeared in fifteen NBA All-Star Games and been named NBA All-Star MVP three times. He won the 2008 NBA scoring title, is the all-time NBA playoffs scoring leader, and is fourth in all-time career points scored. He has been voted onto the All-NBA First Team twelve times and the All-Defensive First Team five times.

James played basketball for St. Vincent–St. Mary High School in his hometown of Akron, Ohio, where he was heavily touted by the national media as a future NBA superstar. A prep-to-pro, he joined the Cleveland Cavaliers in 2003 as the first overall draft pick. Named the 2003–04 NBA Rookie of the Year, he soon established himself as one of the league's premier players; he won the NBA Most Valuable Player Award in 2009 and 2010. After failing to win a championship with Cleveland, James left in 2010 to sign as a free agent with the Miami Heat. This move was announced in an ESPN special titled The Decision, and is one of the most controversial free agent decisions in American sports history.

James won his first two NBA championships while playing for the Miami Heat in 2012 and 2013; in both of these years, he also earned league MVP and Finals MVP. After his fourth season with the Heat in 2014, James opted out of his contract to re-sign with the Cavaliers. In 2016, he led the Cavaliers to victory over the Golden State Warriors in the NBA Finals, delivering the franchise's first championship and ending Cleveland's 52-year professional sports title drought. His teams appeared in the NBA Finals in eight consecutive seasons (from 2011 to 2018). In 2018, James opted out of his contract with the Cavaliers to sign with the Lakers.

Off the court, James has accumulated additional wealth and fame from numerous endorsement contracts. His public life has been the subject of much scrutiny, and he has been ranked as one of America's most influential and popular athletes. He has been featured in books, documentaries, and television commercials. He has also hosted the ESPY Awards and Saturday Night Live, and appeared in the 2015 film Trainwreck.

Miami Heat

The Miami Heat are an American professional basketball team based in Miami, Florida. The Heat compete in the National Basketball Association (NBA) as a member of the league's Eastern Conference Southeast Division. The Heat play their home games at American Airlines Arena, and have won three NBA championships.

The franchise began play in 1988 as an expansion team. After a period of mediocrity, the Heat would gain relevance during the 1990s following the appointment of former head coach Pat Riley in the role of team president. Riley would construct the high-profile trades of Alonzo Mourning in 1995, and of Tim Hardaway in 1996, which immediately propelled the team into playoff contention. Mourning and Hardaway would eventually lead the Heat to four division titles, prior to their departures in 2001 and 2002, respectively. As a result, the team struggled, and entered into a rebuild in time for the 2002–03 season.

Led by Dwyane Wade, and following a trade for former NBA Most Valuable Player (MVP) Shaquille O'Neal, Miami advanced to play in the NBA Finals in 2006, where they clinched their first championship, led by Riley as head coach. After the departure of O'Neal two years later, the team entered into another period of decline for the remainder of the 2000s. This saw the resignation of Riley as head coach, who returned to his position as team president, and was replaced by Erik Spoelstra.

In 2010, after creating significant cap space, the Heat partnered Wade with former league MVP LeBron James, and perennial NBA All-Star Chris Bosh, creating the "Big Three". During their four-year spell together, and under the guise of Spoelstra, James, Wade, and Bosh, they would lead the Heat to the NBA Finals in every season, and won two back-to-back championships in 2012 and 2013. The trio would all depart by 2016, and the team entered another period of rebuilding. Wade was eventually reacquired in 2018, albeit to retire with the franchise.The Heat hold the record for the NBA's third-longest winning streak, 27 straight games, set during the 2012–13 season. Four Hall of Famers have played for Miami, while James has won the NBA MVP Award while playing for the team.

Oil

An oil is any nonpolar chemical substance that is a viscous liquid at ambient temperatures and is both hydrophobic (does not mix with water, literally "water fearing") and lipophilic (mixes with other oils, literally "fat loving"). Oils have a high carbon and hydrogen content and are usually flammable and surface active.

The general definition of oil includes classes of chemical compounds that may be otherwise unrelated in structure, properties, and uses. Oils may be animal, vegetable, or petrochemical in origin, and may be volatile or non-volatile. They are used for food (e.g., olive oil), fuel (e.g., heating oil), medical purposes (e.g., mineral oil), lubrication (e.g. motor oil), and the manufacture of many types of paints, plastics, and other materials. Specially prepared oils are used in some religious ceremonies and rituals as purifying agents.

Scoville scale

The Scoville scale is a measurement of the pungency (spiciness or "heat") of chili peppers and other spicy foods, as recorded in Scoville Heat Units (SHU) based on the concentration of capsaicinoids, among which capsaicin is the predominant component. The scale is named after its creator, American pharmacist Wilbur Scoville, whose 1912 method is known as the Scoville organoleptic test. The Scoville organoleptic test is the most practical method for estimating SHU and is a subjective assessment derived from the capsaicinoid sensitivity by people experienced with eating hot chilis.An alternative method, using high-performance liquid chromatography (HPLC) can be used to analytically quantify the capsaicinoid content as an indicator of pungency. As of 2011, the subjective organoleptic test has been largely superseded by analytical methods such as chromatography.

Shaquille O'Neal

Shaquille Rashaun "Shaq" O'Neal ( shə-KEEL; SHAK; born March 6, 1972) is a retired professional American basketball player who is a sports analyst on the television program Inside the NBA on TNT. He is considered one of the greatest players in National Basketball Association (NBA) history. At 7 ft 1 in (2.16 m) tall and 325 pounds (147 kg), he was one of the tallest and heaviest players ever. O'Neal played for six teams over his 19-year career.

Following his time at Louisiana State University, O'Neal was drafted by the Orlando Magic with the first overall pick in the 1992 NBA draft. He quickly became one of the best centers in the league, winning Rookie of the Year in 1992–93 and leading his team to the 1995 NBA Finals. After four years with the Magic, O'Neal signed as a free agent with the Los Angeles Lakers. They won three consecutive championships in 2000, 2001, and 2002. Amid tension between O'Neal and Kobe Bryant, O'Neal was traded to the Miami Heat in 2004, and his fourth NBA championship followed in 2006. Midway through the 2007–2008 season he was traded to the Phoenix Suns. After a season-and-a-half with the Suns, O'Neal was traded to the Cleveland Cavaliers in the 2009–10 season. O'Neal played for the Boston Celtics in the 2010–11 season before retiring.O'Neal's individual accolades include the 1999–2000 MVP award, the 1992–93 NBA Rookie of the Year award, 15 All-Star game selections, three All-Star Game MVP awards, three Finals MVP awards, two scoring titles, 14 All-NBA team selections, and three NBA All-Defensive Team selections. He is one of only three players to win NBA MVP, All-Star game MVP and Finals MVP awards in the same year (2000); the other players are Willis Reed in 1970 and Michael Jordan in 1996 and 1998. He ranks 8th all-time in points scored, 6th in field goals, 15th in rebounds, and 8th in blocks. Largely due to his ability to dunk the basketball, O'Neal also ranks third all-time in field goal percentage (58.2%). O'Neal was elected into the Naismith Memorial Basketball Hall of Fame in 2016. He was elected to the FIBA Hall of Fame in 2017.In addition to his basketball career, O'Neal has released four rap albums, with his first, Shaq Diesel, going platinum. O'Neal is also an electronic music producer, and touring DJ, known as DIESEL. He has appeared in numerous films and has starred in his own reality shows, Shaq's Big Challenge and Shaq Vs.. He hosts The Big Podcast with Shaq. He is also the general manager of Kings Guard Gaming of the NBA 2K League.

Temperature

A temperature expresses hot and cold, as measured with a thermometer. In physics, hotness is a body's ability to impart energy as heat to another body that is colder.

In a body in which there are processes of chemical reaction and flow of matter, temperature may vary over its parts, and over time, as measured by a suitably small and rapidly responding thermometer, and may depend also on the match of the processes to the characteristics of the thermometer.

There are various temperature scales that nearly or approximately agree with one another, but differ slightly because of the various characteristics of particular thermometric substances. The most commonly used scales are the Celsius scale (formerly called centigrade) (denoted °C), Fahrenheit scale (denoted °F), and Kelvin scale (denoted K).

When a body has no macroscopic chemical reactions or flows of matter or energy, it is said to be in its own internal state of thermodynamic equilibrium. Its temperature is uniform in space and unchanging in time. Then, referring to the Boltzmann constant, a temperature scale is defined and said to be absolute because it is independent of the characteristics of particular thermometric substances and thermometer mechanisms. This is the Kelvin or thermodynamic scale, widely used in science and technology. The kelvin (the word is spelled with a lower-case k) is the unit of temperature in the International System of Units (SI). The thermodynamic temperature is always positive, relative to an absolute zero.

For some conditions other than thermodynamic equilbrium, a suitable thermometer calibrated on the thermodynamic scale, including absolute zero, can register a negative temperature; such conditions are hotter than absolute zero.

Temperature is important in all fields of natural science, including physics, chemistry, Earth science, medicine, and biology, as well as most aspects of daily life.

Thermal conductivity

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by , , or .

Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating materials like Styrofoam. Correspondingly, materials of high thermal conductivity are widely used in heat sink applications and materials of low thermal conductivity are used as thermal insulation. The reciprocal of thermal conductivity is called thermal resistivity.

The defining equation for thermal conductivity is , where is the heat flux, is the thermal conductivity, and is the temperature gradient. This is known as Fourier's Law for heat conduction. Although commonly expressed as a scalar, the most general form of thermal conductivity is a second-rank tensor. However, the tensorial description only becomes necessary in materials which are anisotropic.

Thermodynamics

Thermodynamics is the branch of physics that deals with heat and temperature, and their relation to energy, work, radiation, and properties of matter. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering, but also in fields as complex as meteorology.

Historically, thermodynamics developed out of a desire to increase the efficiency of early steam engines, particularly through the work of French physicist Nicolas Léonard Sadi Carnot (1824) who believed that engine efficiency was the key that could help France win the Napoleonic Wars. Scots-Irish physicist Lord Kelvin was the first to formulate a concise definition of thermodynamics in 1854 which stated, "Thermo-dynamics is the subject of the relation of heat to forces acting between contiguous parts of bodies, and the relation of heat to electrical agency."

The initial application of thermodynamics to mechanical heat engines was extended early on to the study of chemical compounds and chemical reactions. Chemical thermodynamics studies the nature of the role of entropy in the process of chemical reactions and has provided the bulk of expansion and knowledge of the field. Other formulations of thermodynamics emerged. Statistical thermodynamics, or statistical mechanics, concerns itself with statistical predictions of the collective motion of particles from their microscopic behavior. In 1909, Constantin Carathéodory presented a purely mathematical approach in an axiomatic formulation, a description often referred to as geometrical thermodynamics.

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