Heat

For other uses, see Heat (disambiguation).
Heat generated from the nuclear fusion in the Sun, and transported to Earth as electromagnetic radiation, is one of the driving forces of life on Earth.

Heat is energy transferred from one system to another by thermal interaction.[1][2] In contrast to work, heat is always accompanied by a transfer of entropy. Heat flow is characteristic of macroscopic objects and systems, but its origin and properties can be understood in terms of their microscopic constituents.

Heat flow from a high to a low temperature body occurs spontaneously. This flow of energy can be harnessed and converted into useful work by means of a heat engine. The second law of thermodynamics prohibits heat flow from a low to a high temperature body, but with the aid of a heat pump external work can be used to transport energy from low to the high temperature.

The SI unit of heat is the joule. Heat can be measured by calorimetry,[3] or determined indirectly by calculations based on other quantities, relying for instance on the first law of thermodynamics.

Heat transfer can occur in a variety of ways: by conduction[4], radiation,[5]convection, net mass transfer, friction or viscosity,[6] and by chemical dissipation.[7][8][9]

In physics, especially in calorimetry, and in meteorology, the concepts of latent heat and of sensible heat are used. Latent heat is associated with phase changes, while sensible heat is associated with temperature change.

Because in physics it is by definition a transfer of energy, heat is always associated with a process of some kind, and "heat" is used interchangeably with "heat flow" and "heat transfer". In ordinary language, heat has a diversity of meanings, including temperature.[10]

Overview

Heat may flow across the boundary of the system and thus change its internal energy.

The present article is about heat in physics, for which heat is defined as energy transferred to the system by thermal interactions. Heat flows spontaneously from systems of higher temperature to systems of lower temperature. When two systems come into thermal contact, they exchange thermal energy due to the microscopic interactions of their particles. When the systems are at different temperatures, the net flow of thermal energy is not zero and is directed from the hotter region to the cooler region, until their temperatures are equal and the net flow of energy is zero. Spontaneous heat transfer is an irreversible process, which leads to the systems coming closer to mutual thermodynamic equilibrium.

The first law of thermodynamics requires that the energy of an isolated system is conserved. To change the energy of a system, energy must be transferred to or from the system. For a closed system, heat and work are the mechanisms by which energy can be transferred. For an open system, total energy can be changed also by transfer of matter.[11] Work performed on a system is, by definition [12], an energy transfer to the system that is due to a change to external or mechanical parameters of the system, such as the volume, magnetization, center of mass in a gravitational field.

In a thermodynamic sense, heat is never regarded as being stored within a system. Like work, it exists only as energy in transit from one system to another or between a system and its surroundings. When energy in the form of heat is added to a system, it is stored as kinetic and potential energy of the atoms and molecules in the system.[13]

Definitions

Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of many who began to build on the already established idea that heat was something to do with matter in motion. This was the same idea put forwards by Sir Benjamin Thompson in 1798, who said he was only following on from the work of many others. One of Maxwell's recommended books was by John Tyndall Heat as a Mode of Motion. Maxwell outlined four stipulations for the definition of heat:

Mechanisms of heat transfer

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."[14]

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."[15]

From these empirically based ideas of heat and from other empirical observations, the notions of internal energy and of entropy can be derived, so as to lead to the recognition of the first and second laws of thermodynamics.[16] This was the way of the historical pioneers of thermodynamics.[17][18]

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 joules per second.

The total amount of energy transferred as heat is conventionally written as Q for algebraic purposes. 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 \dot{Q}. 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. Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in the unit watts per square metre.

Estimation of quantity of heat

The quantity of heat transferred by some process can either be directly measured, or determined indirectly through calculations based on other quantities.

Direct measurement is by calorimetry and is the primary empirical basis of the idea of quantity of heat. 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.[19][20]

Indirect estimations heat rely on the law of conservation of energy, and in particular cases on the first law of thermodynamics. Indirect estimation is the primary approach of many theoretical studies of heat.[21][22][23]

Internal energy and enthalpy

In the case where the number of particles in the system is constant (closed systems), the first law of thermodynamics states that the differential change in internal energy dU of a system is given by an infinitesimal amount of heat δQ supplied to the system minus the infinitesimal amount of work δW exerted by the system:[note 1]

\mathrm{d} U = \delta Q - \delta W \quad{\rm{(first\,\,law)}}.

This can also be interpreted as that δQ makes contributions to the internal energy and to the work done by the system:

\delta Q = \mathrm{d} U + \delta W.

The work, done by the system, includes boundary work, caused the expanding boundaries of the system (usually a piston), in addition to other work (e.g. shaft work performed by a compressor fan):

\delta Q = \mathrm{d} U + \delta W_\text{boundary} + \delta W_\text{other}.

In this Section we will neglect the "other-work" contribution. The internal energy, U, is a state function. In cyclical processes, such as the operation of a heat engine, state functions return to their initial values after completing one cycle. Thus, the differential for the internal energy is an exact differential dU. The symbol for exact differentials is the lowercase letter d.

In contrast, neither Q nor W represents the state of the system. Thus, infinitesimal amounts of heat and work are inexact differentials, denoted by δQ and δW, respectively. 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. However, if heat is supplied to a system in which no irreversible processes take place and which has a well-defined temperature T, the heat δQ and the temperature T form the exact differential

\mathrm{d}S =\frac{\delta Q}{T},

with S the entropy of the system. Likewise, with a well-defined pressure p behind the moving boundary, the work δW and the pressure p form the exact differential

\mathrm{d}V =\frac{\delta W}{p},

with V the volume of the system. In general, for homogeneous systems,

\mathrm{d}U = T\mathrm{d}S - p\mathrm{d}V.

If V is constant

T\mathrm{d}S=\mathrm{d}U \text{ (V constant)}

and if p is constant

T\mathrm{d}S=\mathrm{d}H \text{ (p constant)}

with H the enthalpy given by

H=U+pV.

Path-independent examples for an ideal gas

For a simple compressible system such as an ideal gas inside a piston, the internal energy change ΔU at constant volume and the enthalpy change ΔH at constant pressure are modeled by separate heat capacity values, which are CV and Cp, respectively.

Constrained to have constant volume, the heat, Q, required to change its temperature from an initial temperature, T0, to a final temperature, Tf, is given by

Q = \int_{T_0}^{T_f}C_V\mathrm{d}T = \Delta U.

Allowing the system to expand or contract at constant pressure, the heat, Q, required to change its temperature from an initial temperature, T0, to a final temperature, Tf, is given by

Q = \int_{T_0}^{T_f}C_p \mathrm{d}T = \Delta U + \int_{V_0}^{V_f}p\mathrm{d}V = \Delta H.

Here we used the definition of the enthalpy and the fact that p is constant. When integrating an exact differential (e.g. dU), the lowercase letter d is substituted for Δ (e.g. ΔU). Note that the symbol Δ is convenient since it is compact, but it can lead to sign errors. So it may be better to write Uf - U0 instead of ΔU.

When integrating an inexact differential (e.g. δQ), the lowercase Greek letter δ is removed with no replacement (e.g. Q).

Latent and sensible heat

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.[24] 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 or what was known as a living force. At the time of Joule kinetic energy either held 'invisibly' internally or held 'visibly' externally was known as a living force.

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.[25][26] The term was introduced around 1750 by Joseph Black as derived from the Latin latere (to lie hidden), characterizing its effect as not being directly measurable with a thermometer.

Sensible heat, in contrast to latent heat, is the heat exchanged by a thermodynamic system that has as its sole effect a change of temperature.[27] Sensible heat therefore only increases the thermal energy of a system.

Consequences of Black's distinction between sensible and latent heat are examined in the Wikipedia article on calorimetry.

Specific heat

Specific heat, also called specific heat capacity, is defined as the amount of energy that has to be transferred to or from one unit of mass (kilogram) or amount of substance (mole) to change the system temperature by one degree. Specific heat is a physical property, which means that it depends on the substance under consideration and its state as specified by its properties.

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

Microscopic origin of heat

Heat is a macroscopic characteristic of systems, but like other thermodynamic quantities it has a microscopic explanation given by statistical mechanics. Temperature in many systems is the kinetic energy of motion of microscopic particles, and heat is the exchange of such energy. An early and vague expression of this was by Francis Bacon.[28][29] Precise and detailed versions of it were developed in the nineteenth century.[30]

Entropy

Main article: Entropy
Rudolf Clausius

In 1856, German physicist Rudolf Clausius 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:"[31][32]

{} \frac {Q}{T}.

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

\Delta S = \frac {Q}{T}

and thus, for small changes, quantities of heat δQ (an inexact differential) are defined as quantities of TdS, with dS an exact differential:

\delta Q = T \mathrm{d}S .

This equality is only valid for a closed system and if no irreversible processes take place inside the system while the heat δQ is applied. If, in contrast, irreversible processes are involved, e.g. some sort of friction, then there is entropy production and, instead of the above equation, one has

\delta Q \leq T \mathrm{d}S \quad{\rm{(second\,\,law)}}\,.

This is the second law of thermodynamics for closed systems.

Heat transfer in engineering

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 includes the mechanisms of heat conduction, thermal radiation, and mass transfer. In engineering, the term convective heat transfer is used to describe the combined effects of conduction and fluid flow and is often regarded as an additional mechanism of heat transfer. Although distinct physical laws may describe the behavior of each of these methods, real systems often exhibit a complicated combination which are often described by a variety of complex mathematical methods.

Practical applications

In accordance with the first law, heat may be converted to or from work.

Heat engines operate by converting heat flow from a high temperature reservoir to a low temperature reservoir into work. One example are steam engines, where the high temperature reservoir is steam generated by boiling water. The flow of heat from the hot steam to water is converted into mechanical work via a turbine or piston. Heat engines achieve high efficiency when the difference between initial and final temperature is high.

Heat pumps, by contrast, use work to cause thermal energy to flow from low to high temperature, the opposite direction heat would flow spontaneously. An example is a refrigerator or air conditioner, where electric power is used to cool a low temperature system (the interior of the refrigerator) while heating a higher temperature environment (the exterior). High efficiency is achieved when the temperature difference is small.

See also

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Notes

  1. ^ An alternate convention is to consider the work performed on the system by its surroundings. This leads to a change in sign of the work. 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.

References

  1. ^ Reif, F. (1965), pp. 67, 73.
  2. ^ Kittel, C. Kroemer, H. (1980). Thermal Physics, second edition, W.H. Freeman, San Francisco, ISBN 0-7167-1088-9, p. 227.
  3. ^ Maxwell 1871, Chapter III.
  4. ^ Guggenheim, E.A. (1949/1967).
  5. ^ Planck. M. (1914). The Theory of Heat Radiation, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.
  6. ^ Lebon, G., Jou, D., Casas-Vásquez, J. (2008). Understanding Non-equilibrium Thermodynamics. Foundations, Applications, Frontiers, Springer, ISBN 978–3–540–74252–4, pages 120 and 62.
  7. ^ Planck 1927.
  8. ^ Partington, J.R. (1949)
  9. ^ Guggenheim, E.A. (1949/1967)
  10. ^ Oxford English Dictionary, second edition, Oxford University Press, Oxford, UK.
  11. ^ Kondepudi, D. (2008)
  12. ^ Reif, F. (1965), p. 73.
  13. ^ Smith, J.M., Van Ness, H.C., Abbot, M.M. (2005). Introduction to Chemical Engineering Thermodynamics. McGraw-Hill. ISBN 0073104450. 
  14. ^ Partington, J.R. (1949), p. 118.
  15. ^ Maxwell, J.C. (1871), p. 10.
  16. ^ Planck, M. (1903).
  17. ^ Partington, J.R. (1949).
  18. ^ Truesdell, C. (1980), page 15.
  19. ^ Maxwell J.C. (1872), p. 54.
  20. ^ Planck (1927), Chapter 3.
  21. ^ Bryan, G.H. (1907), p. 47.
  22. ^ C. Carathéodory (1909). "Untersuchungen über die Grundlagen der Thermodynamik". Mathematische Annalen 67: 355–386. A partly reliable translation is to be found at Kestin, J. (1976). The Second Law of Thermodynamics, Dowden, Hutchinson & Ross, Stroudsburg PA.. 
  23. ^ Callen, H.B. (1960/1985). Thermodynamics and an Introduction to Thermostatistics, second edition, John Wiley & Sons, New York, ISBN 0-471-86256-8, Section 1–8.
  24. ^ J. P. Joule (1884), The Scientific Paper of James Prescott Joule, The Physical Society of London, p. 274, "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." , Lecture on Matter, Living Force, and Heat. May 5 and 12, 1847
  25. ^ Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6. 
  26. ^ Clark, John, O.E. (2004). The Essential Dictionary of Science. Barnes & Noble Books. ISBN 0-7607-4616-8. 
  27. ^ Ritter, Michael E. (2006). "The Physical Environment: an Introduction to Physical Geography". http://www.uwsp.edu/geo/faculty/ritter/geog101/textbook/energy/energy_balance.html. 
  28. ^ Bacon, F. (1620). Novum Organum Scientiarum, translated by Devey, J., P.F. Collier & Son, New York, 1902.
  29. ^ Partington, J.R. (1949), page 131.
  30. ^ Partington, J.R. (1949), pages 132–136.
  31. ^ Published in 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
  32. ^ Clausius, R. (1865). The Mechanical Theory of Heat] –with its Applications to the Steam Engine and to Physical Properties of Bodies. London: John van Voorst, 1 Paternoster Row. MDCCCLXVII.

Bibliography

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