Heat

For other uses, see Heat (disambiguation).

In physics, chemistry, engineering, and thermodynamics, heat is energy produced or transferred from one body, region, set of components, or thermodynamic system to another in any way other than as thermodynamic work.[1]

In ordinary language, as distinct from technical language, heat has a broader meaning.[2] This can lead to confusion if the diversity of usage of words is forgotten.[3][4]

Thermodynamically, energy can be produced or transferred as heat by thermal conduction[5], by thermal radiation[6], by friction and viscosity,[7] and by chemical dissipation[8].

The engineering discipline of heat transfer recognizes heat transfer by thermal conduction, by convection, through mass transfer of fluid, and by thermal radiation.

Heat transfer by conduction and by radiation from a hotter to a colder body is spontaneous. The second law of thermodynamics requires that the transfer of energy from one body to another with an equal or higher temperature can only occur with the aid of a heat pump by mechanical work, or by some other similar process in which entropy is increased in the universe in a manner that compensates for the decrease of entropy in the cooled body, due to the removal of the heat from it.[9] For example, energy may be removed against a temperature gradient by spontaneous evaporation of a liquid.

In physics, especially in calorimetry, and in meteorology, the concepts of latent heat and of sensible heat are used.

A related and potentially confusing term is thermal energy, loosely defined as the energy of a body that increases with its temperature. Potentially confusingly, thermal energy is sometimes referred to as heat, although the thermodynamic definition of heat requires it to be in transfer between two systems or in production in a dissipative process such as friction, viscosity, or chemical reaction.

Contents

Overview

Heat flows spontaneously only from systems of higher temperature to systems of lower temperature. When two systems come into thermal contact, they always 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 flow of heat ceases. Then they have reached a state of thermal equilibrium, exchanging thermal energy at an equal rate in both directions.

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.

Work performed on a system is, by definition [1], 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.

For a closed system (with no external transfer of matter), heat is defined as energy transferred to the system in any way other than as work. Heat transfer is an irreversible process, which leads to the systems coming closer to mutual thermodynamic equilibrium. In the case of systems close to thermodynamic equilibrium where temperature can be defined, some heat transfer can be related to temperature difference between systems. Heat transfer can also arise by friction and by viscosity. For an open system, far from thermodynamic equilibrium, where temperature cannot be defined, there the distinction between heat and work may not be feasible.

Human notions such as hot and cold are relative terms and are generally used to compare one system’s temperature to another or its surroundings.

Definitions

Scottish physicist James Clerk Maxwell, in his 1871 classic Theory of Heat, was one of the first to enunciate a modern definition of heat. Maxwell outlined four stipulations for the definition of heat:

Several modern definitions of heat are as follows:

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.[12]

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} = {dQ\over dt} \,\!.

Heat flux is defined as rate of heat transfer per unit cross-sectional area, resulting in the unit watts per square metre.

Semantics

There is some diversity of usage of the word heat, even in technical scientific writings.[13] In current scientific usage, the language surrounding the term can be conflicting and even misleading. One study showed that several popular textbooks used language that implied several meanings of the term, that heat is the process of transferring energy, that it is the transferred energy (i.e., as if it were a substance), and that is an entity contained within a system, among other similar descriptions. The study determined it was not uncommon for a combination of these representations to appear within the same text.[14] They found the predominant use among physicists to be as if it were a substance.

Internal energy and enthalpy

In the case where the number of particles in the system is constant, the first law of thermodynamics states that the differential change in internal energy dU of a system is given by the differential heat flow δQ into the system minus the differential work δW exerted by the system:[note 1]

\mathrm{d} U = \delta Q_\text{in} - \delta W_\text{out} \quad{\rm{(first\,\,law)}} ,

The differential transfer of heat, \delta Q_\text{in}, makes differential contributions, not only to internal energy, but also to the work done by the system:

\delta Q_\text{in} = \mathrm{d} U %2B \delta W_\text{out} \ ,

The work done by the system includes boundary work, which causes the boundaries of the system to expand, in addition to other work (e.g. shaft work performed by a compressor fan):

\delta Q_\text{in} = \mathrm{d} U %2B \delta W_\text{boundary} %2B \delta W_\text{other} \ ,

\mathrm{d} U %2B \delta W_\text{boundary}\ is equal to the differential enthalpy change (dH) of the system. Substitution gives:

\delta Q_\text{in} = \mathrm{d} H %2B \delta W_\text{other} \ ,

Both enthalpy, H, and internal energy, U, are state functions. In cyclical processes, such as the operation of a heat engine, state functions return to their initial values. Thus, the differentials for enthalpy and energy are exact differentials, which are dH and dU, respectively. The symbol for exact differentials is the lowercase letter d.

In contrast, neither Q nor W represents the state of the system (i.e. they need not return to their original values when returning to same step in the following cycle). Thus, the infinitesimal expressions for heat and work are inexact differentials, \delta Q and \delta W, respectively. The lowercase Greek letter delta, \delta, is the symbol for inexact differentials. The integral of any inexact differential over the time it takes to leave and return to the same thermodynamic state does not necessarily equal zero. However, for slow enough processes involving no change in volume (i.e. dV = 0), applied magnetic field, or other external parameters (i.e. \delta W_\text{out} = 0 and \delta W_\text{in} = 0), \delta Q forms the exact differential, dS = \frac{\delta Q_\text{rev}}{T}, wherein the following relation applies:

dU = TdS = \delta Q_\text{rev}.

Likewise, for an isentropic process (i.e. \delta Q = 0 and dS = 0), \delta W forms the exact differential, dV = \frac{\delta W_\text{rev}}{p}, wherein the following relation applies:

dU = - pdV = - \delta W_\text{rev},

Path-independent examples for an ideal gas

For a simple compressible system such as an ideal gas inside a piston, the internal energy change \Delta U at constant volume and the enthalpy change \Delta H at constant pressure are modeled by separate heat capacity values, which are C_v and C_p, 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 this formula:

Q = \int_{T_0}^{T_f}C_v\,dT = \Delta U\,\!

Removing the volume constraint and 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 this formula:

Q = \int_{T_0}^{T_f}C_p\,dT = \Delta U %2B W_\text{boundary} = \Delta U %2B \int_{V_0}^{V_f}P\,dV\,\! = \Delta H

Note that when integrating an exact differential (e.g. \mathrm{d} U), the lowercase letter d is substituted for \Delta (e.g. \Delta U), and when integrating an inexact differential (e.g. \delta W_{boundary}), the lowercase Greek letter \delta is removed with no replacement (e.g. W_{boundary}). z

Incompressible substances

For incompressible substances, such as solids and liquids, the distinction between the two types of heat capacity (i.e. C_p which is based on constant pressure and C_v which is based on constant volume) disappears, as no work is performed.

Latent and sensible heat

In a 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 effecting distinct physical phenomena, namely the potential and kinetic energy of particles, respectively.[15] He described latent energy as the energy of interaction in a given configuration of particles, i.e. a form of potential energy, and the sensible heat as an energy affecting the thermal energy, which he called the 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.[16][17] 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.[18] 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.

Entropy

Main article: Entropy

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:"[19][20]

{} \frac {Q}{T}

In 1865, he came to define this ratio as entropy symbolized by S, such that, for a closed, stationary system:

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

and thus, by reduction, quantities of heat δQ (an inexact differential) are defined as quantities of TdS (an exact differential):

\delta Q = T dS \,

In other words, the entropy function S facilitates the quantification and measurement of heat flow through a thermodynamic boundary.

To be precise, this equality is only valid, if the heat \delta Q is applied reversibly. If, in contrast, irreversible processes are involved, e.g. some sort of friction, then instead of the above equation one has

\delta Q \leq T dS \quad{\rm{(second\,\,law)}}\,.

This is the second law of thermodynamics.

Heat transfer in engineering

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.

Application

In accordance with the first law, heat may be converted to or from work by so-called heat engines, e.g. the steam engine. Heat engines achieve maximum efficiency when the difference between initial and final temperature is largest, resulting in minimal loss. Heat pumps on the other hand operate at a small temperature difference, transferring heat at low temperatures from a reservoir, e.g. from the soil, and deliver it by means of electrical work for heating purposes. Now the temperature difference should be small, to keep the lost electrical work small.

See also

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. ^ a b F. Reif (2000). Fundamentals of Statistical and Thermal Physics. Singapore: McGraw-Hll, Inc.. p. 67. ISBN 0-07-Y85615-X. 
  2. ^ Oxford English Dictionary, second edition, Oxford University Press, Oxford, UK.
  3. ^ Planck, M. (1897/1903). Treatise on Thermodynamics, translated by A. Ogg, Longmans, Green & Co., London, page 1: "This direct sensation, however, furnishes no quantitative scientific measure ..."
  4. ^ Truesdell, C. (1980). The Tragicomical History of Thermodynamics 1822-1854, Springer, New York, ISBN 0–387–90403–4, page 15: "What they meant is not always clear."
  5. ^ Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, fifth edition, North-Holland Publishing, Amsterdam, page 8.
  6. ^ Planck. M. (1914). The Theory of Heat Radiation, a translation by Masius, M. of the second German edition, P. Blakiston's Son & Co., Philadelphia.
  7. ^ 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.
  8. ^ Guggenheim, E.A. (1949/1967). Thermodynamics. An Advanced Treatment for Chemists and Physicists, fifth edition, North-Holland Publishing, Amsterdam, pages 241–242.
  9. ^ Planck, M. (1922/1927). Treatise on Thermodynamics, third English edition, translated from the seventh German edition by Ogg, A., Longmans, Green & Co., Ltd., London, page 89.
  10. ^ Discourse on Heat and Work - Department of Physics and Astronomy, Georgia State University: Hyperphysics (online)
  11. ^ Schroeder, Daniel V. (2000). An introduction to thermal physics. San Francisco, California: Addison-Wesley. p. 18. ISBN 0-321-27779-1. "Heat is defined as any spontaneous flow of energy from one system to another, caused by a difference in temperature between the systems." 
  12. ^ Smith, J.M., Van Ness, H.C., Abbot, M.M. (2005). Introduction to Chemical Engineering Thermodynamics. McGraw-Hill. ISBN 0073104450. 
  13. ^ "A review of selected literature on students' misconceptions of heat". Boğaziçi University Journal of Education 20 (1): 25–41. 2003. http://buje.boun.edu.tr/upload/revizeedilmis/45bc61ceeb94344a0664C646d01.pdf. 
  14. ^ Brookes, D.; Horton, G.; Van Heuvelen, A.; Etkina, E. (2005). "Concerning Scientific Discourse about Heat". 2004 Physics Education Research Conference (AIP Conference Proceedings) 790: 149–152. doi:10.1063/1.2084723. http://research.physics.illinois.edu/per/David/perc2004_revised.pdf. 
  15. ^ J. P. Joule (1884), The Scientific Paper of James Prescott Joule, The Physical Society of London, p. 274, "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
  16. ^ Perrot, Pierre (1998). A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6. 
  17. ^ Clark, John, O.E. (2004). The Essential Dictionary of Science. Barnes & Noble Books. ISBN 0-7607-4616-8. 
  18. ^ 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. 
  19. ^ 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
  20. ^ 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.

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