Thermal energy

The term "thermal energy" is often used ambiguously in physics and engineering.^[1] It can denote several different physical concepts, including:

Internal energy: The total energy contained within a body of matter or radiation.
Heat: Energy in transfer between a system and its surroundings by mechanisms other than thermodynamic work and transfer of matter.
The characteristic energy $k B T$ associated with a single microscopic degree of freedom, where $T$ denotes temperature and $k B$ denotes the Boltzmann constant.

Mark Zemansky (1970) has argued that the term “thermal energy” is best avoided due to its ambiguity. He suggests using more precise terms like “internal energy” and “heat” to avoid confusion.^[1] The term is, however, used in some textbooks.^[2]

Relation between heat and internal energy

In thermodynamics, heat is energy in transfer to or from a thermodynamic system by mechanisms other than thermodynamic work or transfer of matter, such as conduction, radiation, and friction.^[3]^[4] Heat refers to a quantity in transfer between systems, not to a property of any one system, or "contained" within it; on the other hand, internal energy and enthalpy are properties of a single system. Heat and work depend on the way in which an energy transfer occurs, whereas internal energy is a property of the state of a system and can thus be understood without knowing how the energy got there.^[5]

Macroscopic thermal energy

When the term 'thermal energy' refers to the internal energy of a body, in addition to the microscopic kinetic energies of its molecules, one can think of chemical energy belonging to distinct molecules, and of global joint energy involved in the interactions between molecules and suchlike. Such thermal energy may be viewed as contributing to internal energy or to enthalpy, thinking of the contribution as a process without thinking that the contributed energy has become an identifiable component of the internal or enthalpic energies.^[6]^{[failed verification]}

Chemical internal energy

The internal energy of a body can change in a process in which chemical potential energy is converted into non-chemical energy. In such a process, the thermodynamic system can change its internal energy by doing work on its surroundings, or by gaining or losing energy as heat. It is not quite lucid to merely say that "the converted chemical potential energy has simply become internal energy". It is, however, sometimes convenient to say that "the chemical potential energy has been converted into thermal energy". This is expressed in ordinary traditional language by talking of 'heat of reaction'.^[7]

Potential energy of internal interactions

In a body of material, especially in condensed matter, such as a liquid or a solid, in which the constituent particles, such as molecules or ions, interact strongly with one another, the energies of such interactions contribute strongly to the internal energy of the body, but are not immediately apparent in the kinetic energies of molecules, as manifest in temperature. Such energies of interaction may be thought of as contributions to the global internal microscopic potential energies of the body.^[8]

Microscopic thermal energy

In a statistical mechanical account of an ideal gas, in which the molecules move independently between instantaneous collisions, the internal energy is just the sum total of the gas's independent particles' kinetic energies, and it is this kinetic motion that is the source and the effect of the transfer of heat across a system's boundary. For a gas that does not have particle interactions except for instantaneous collisions, the term "thermal energy" is effectively synonymous with "internal energy".^[9]

In many statistical physics texts, "thermal energy" refers to $kT$ , the product of the Boltzmann constant and the absolute temperature, also written as $k_{\text{B}}T$ .^[10]^[11]^[12]^[13]

Thermal current density

When there is no accompanying flow of matter, the term "thermal energy" is also applied to the energy carried by a heat flow.^[14]

References

^ ^a ^b Zemansky, Mark W. (1970-09-01). "The Use and Misuse of the Word "Heat" in Physics Teaching". The Physics Teacher. 8 (6): 295–300. doi:10.1119/1.2351512. ISSN 0031-921X.
^ For example: Knight, Randall Dewey (2008). Physics for Scientists and Engineers. San Francisco: Pearson Addison Wesley. ISBN 978-0-8053-2736-6. OCLC 148732206.
^ Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 82.
^ Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London, p. 31.
^ Robert F. Speyer (2012). Thermal Analysis of Materials. Materials Engineering. Marcel Dekker, Inc. p. 2. ISBN 978-0-8247-8963-3.
^ Baierlein, R. (1999). Thermal Physics. Cambridge University Press. pp. 8 –. ISBN 978-0-521-65838-6.
^ Anderson, G.M. (2005). Thermodynamics of Natural Systems, 2nd edition, Cambridge University Press, ISBN 978-0-521-84772-8, page 7: "We also note that whatever kind of energy is being reduced (we call it “chemical energy”), it is not simply heat energy."
^ Baierlein, R. (1999). Thermal Physics. Cambridge University Press. ISBN 978-0-521-65838-6. page 8: "intermolecular potential energy (primarily electrical in origin)."
^ Kittel, Charles (2012). Elementary Statistical Physics. Courier Corporation. p. 60. ISBN 9780486138909.
^ Reichl, Linda E. (2016). A Modern Course in Statistical Physics. John Wiley and Sons. p. 154. ISBN 9783527690466.
^ Kardar, Mehran (2007). Statistical Physics of Particles. Cambridge University Press. p. 243. ISBN 9781139464871.
^ Feynman, Richard P. (2000). "The Computing Machines in the Future". Selected Papers of Richard Feynman: With Commentary. World Scientific. ISBN 9789810241315.
^ Feynman, Richard P. (2018). Statistical Mechanics: A Set of Lectures. CRC Press. p. 265. ISBN 9780429972669.
^ Ashcroft, Neil; Mermin, N. David (1976). Solid State Physics. Harcourt. p. 20. ISBN 0-03-083993-9. We define the thermal current density ${\bf {j}}^{q}$ to be a vector parallel to the direction of heat flow, whose magnitude gives the thermal energy per unit time crossing a unit area perpendicular to the flow.

[:0-1] Zemansky, Mark W. (1970-09-01). "The Use and Misuse of the Word "Heat" in Physics Teaching". The Physics Teacher. 8 (6): 295–300. doi:10.1119/1.2351512. ISSN 0031-921X.

[m341-2] For example: Knight, Randall Dewey (2008). Physics for Scientists and Engineers. San Francisco: Pearson Addison Wesley. ISBN 978-0-8053-2736-6. OCLC 148732206.

[3] Bailyn, M. (1994). A Survey of Thermodynamics, American Institute of Physics Press, New York, ISBN 0-88318-797-3, p. 82.

[4] Born, M. (1949). Natural Philosophy of Cause and Chance, Oxford University Press, London, p. 31.

[speyer-5] Robert F. Speyer (2012). Thermal Analysis of Materials. Materials Engineering. Marcel Dekker, Inc. p. 2. ISBN 978-0-8247-8963-3.

[6] Baierlein, R. (1999). Thermal Physics. Cambridge University Press. pp. 8 –. ISBN 978-0-521-65838-6.

[7] Anderson, G.M. (2005). Thermodynamics of Natural Systems, 2nd edition, Cambridge University Press, ISBN 978-0-521-84772-8, page 7: "We also note that whatever kind of energy is being reduced (we call it “chemical energy”), it is not simply heat energy."

[8] Baierlein, R. (1999). Thermal Physics. Cambridge University Press. ISBN 978-0-521-65838-6. page 8: "intermolecular potential energy (primarily electrical in origin)."

[9] Kittel, Charles (2012). Elementary Statistical Physics. Courier Corporation. p. 60. ISBN 9780486138909.

[10] Reichl, Linda E. (2016). A Modern Course in Statistical Physics. John Wiley and Sons. p. 154. ISBN 9783527690466.

[11] Kardar, Mehran (2007). Statistical Physics of Particles. Cambridge University Press. p. 243. ISBN 9781139464871.

[12] Feynman, Richard P. (2000). "The Computing Machines in the Future". Selected Papers of Richard Feynman: With Commentary. World Scientific. ISBN 9789810241315.

[13] Feynman, Richard P. (2018). Statistical Mechanics: A Set of Lectures. CRC Press. p. 265. ISBN 9780429972669.

[14] Ashcroft, Neil; Mermin, N. David (1976). Solid State Physics. Harcourt. p. 20. ISBN 0-03-083993-9. We define the thermal current density ${\bf {j}}^{q}$ to be a vector parallel to the direction of heat flow, whose magnitude gives the thermal energy per unit time crossing a unit area perpendicular to the flow.

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