What Is Heat? Definition in Thermodynamics Explained
One of the most frustrating misconceptions in thermodynamics centers on the actual definition of heat. Many science and engineering students refer to a body as possessing heat, but as we will show below, that phrasing is misleading and technically incorrect.
Table of Contents
First Law of Thermodynamics
The first law is a statement of the principle of conservation of energy and is often written as
ΔU = Q + W
Here ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done on the system. What do these terms mean in practice?
Internal energy
Internal energy is the energy associated with the microscopic degrees of freedom of a system — that is, the energy associated with the random motion and interactions of the molecules in the system.
For a general fluid, the internal energy is the sum of the following microscopic contributions:
- translational kinetic energy of molecules,
- rotational kinetic energy,
- vibrational kinetic energy, and
- intermolecular potential energy.
Internal energy is a state function: the change in internal energy between any two equilibrium states is independent of the path taken. It is incorrect to call internal energy “heat”; heat is a transfer mechanism, not a property the body “possesses.”
Work
If you’re familiar with mechanics, you already have an intuitive sense of work. In thermodynamics, work refers to macroscopic energy transfer that occurs via a generalized force acting through a displacement. A common example is applying a force to a piston to compress a gas in a cylinder — the external agent does work on the gas.
Using the sign convention in the equation above, work done on the system is taken as positive. If the gas expands and pushes the piston outward, the gas does work on the surroundings and W is negative. If the cylinder walls are adiabatic (no heat transfer), all work done on the gas increases its internal energy.
Heat
Temperature provides a useful way to connect microscopic motion with macroscopic observation. A kinetic definition of temperature views it as a measure of the average translational kinetic energy of the particles in a system. Temperature and internal energy are related, but not simply proportional in general, because internal energy also includes rotational, vibrational, and potential contributions.
We can increase a system’s internal energy either by doing work on it or by adding heat. For example, imagine two identical cylinders of gas initially at 373 K. If we compress one cylinder (work) and heat the other (heat) until both are at 473 K and have identical macroscopic properties (pressure, volume, temperature), their final states will be indistinguishable. There is no experiment that can tell which cylinder was compressed and which was heated — only that their internal energies increased.
This thought experiment highlights that heat and work are both modes of energy transfer between system and surroundings, not properties contained within the system.
Formal definition of heat:
“Heat is the non-mechanical exchange of energy between a system and its surroundings that occurs because of a temperature difference.”
Because heat and work describe energy transfer processes, the phrase “a body possesses heat” is misleading: it is better to say a body has internal energy or that energy has been transferred to a body by heat. Likewise, rather than saying “a body’s heat has increased,” say “the body’s internal energy has increased” or “the body has gained energy by heat.”
Sources
Some texts use the term “thermal energy” specifically for the translational kinetic contribution to internal energy; this terminology can sometimes add confusion unless the author defines it precisely.
Further reading
- Finn, C. B. P., Thermal Physics, 2nd Edition.
- Heat — HyperPhysics
- Internal Energy — HyperPhysics
Written by Hootenanny. Edited by berkeman and Kurdt.
This article was authored by several Physics Forums members with PhDs in physics or mathematics.
I beg to differ DrDu. “pressure difference will not only drive a mass current but also a heat current” here. does this statement not make heat the state variable? Heat Current means heat was here and now it is there!
As DrDU talks of non-mechanical exchange of energy as heat, one should also consider non-mechanical work when electrical energy does the work on the system. I think that both heat and work should be dealt equivocally in the perview of Thermodynamics and then point out the essential difference. When an electric heater heats up we may losely say that electrical energy is converted to heat energy. But in the perview of Thermodynamics, Electrical energy is transferred to the heater coil increasing its internal energy raising its temperature above the surrounding which flows as heat to the surrounding. Similar arguments can be given for describing Peltier effect.
I tend to agree with the Starter, but before I read the other comments i would like to submit my composite view of work and heat by saying that both relate to transfer of energy between two systems. Heat is the transferred energy as a result of temperature difference and work is the transfer of energy where temperature is not directly involved. This kind of thinking for work and heat is most suited in the perview of Thermodynamics, which asserts that Heat and work areprocess variables and can be talked about only when two systems are involved. It release the historic mechanistic connection of work with force.
“[IMG]https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcRGN1FuMP_3KBHaRSIcWfMUhSv8PsLDIYjENbIc4IIglnsNeuzA[/IMG] The profile looks like this at the boundaries or the interface of two conducting surfaces. I’m actually lost by the term “continuous”, my apology “english” is not my native tounge.”
Yes. This is more like it. I just wanted to clarify what you were saying. By continuous, what I mean is that the temperature does not change by a finite amount when one crosses the boundary between the two materials.
“At time zero, you place a hot conductive semi-infinite solid slab in contact with an identical cold conductive semi-infinite solid slab, and let nature take its course. What do the temperature profiles look like within the two solids at times t > 0? Is the temperature a continuous function of spatial position, including at the boundary? Is the temperature gradient continuous at the boundary? Is the heat flux continuous at the boundary? What are the temperatures in the slabs far from the boundary? What are the the temperatures at the boundary?
Chet”
[IMG]https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcRGN1FuMP_3KBHaRSIcWfMUhSv8PsLDIYjENbIc4IIglnsNeuzA[/IMG] The profile looks like this at the boundaries or the interface of two conducting surfaces. I’m actually lost by the term “continuous”, my apology “english” is not my native tounge.
“My apology Chet, your q is quite deep. I am not sure I got 100% of what you mean. Could you rephrase or give example, perhaps?”
At time zero, you place a hot conductive semi-infinite solid slab in contact with an identical cold conductive semi-infinite solid slab, and let nature take its course. What do the temperature profiles look like within the two solids at times t > 0? Is the temperature a continuous function of spatial position, including at the boundary? Is the temperature gradient continuous at the boundary? Is the heat flux continuous at the boundary? What are the temperatures in the slabs far from the boundary? What are the the temperatures at the boundary?
Chet
“Temperature is a continuous function of spatial position during an irreversible change, including at the interface between conductive solids and at the interface between real world reservoirs. However, the temperature gradient (heat flux) at the interface does not have to be continuous. Do you agree with this statement?
Chet”
My apology Chet, your q is quite deep. I am not sure I got 100% of what you mean. Could you rephrase or give example, perhaps?
”
No, it’s appropriate to say at the boundary the temperature is in between hot and cold reservoir (whichever is hotter – system or surrounding or vice versa)”
Temperature is a continuous function of spatial position during an irreversible change, including at the interface between conductive solids and at the interface between real world reservoirs. However, the temperature gradient (heat flux) at the interface does not have to be continuous. Do you agree with this statement?
Chet
“In a closed system, no mass crosses the boundary of the system, but still, work can be done.”
Yes, one example is sterling engine. Note that what I said was ” mass or energy”. Also my apology for stating “higher or lower system boundary.” It should be higher or lower system states.
Work can be done on a close system, given that boundary either expands or collapses, otherwise it’s useless. It’s like heating an LPG tank, no matter how much heat you apply on it, you can’t expect any work until it explodes.
“You are saying that heat cannot be transferred to a system unless there is a temperature gradient at the boundary, correct? Certainly, at the boundary, the temperature of the system must match the temperature of the surroundings (i.e., temperature is continuous at the boundary).”
No, it’s appropriate to say at the boundary the temperature is in between hot and cold reservoir (whichever is hotter – system or surrounding or vice versa)
“Analysis on boundary, surrounding and system might clear out confusions. Both work and heat are boundary phenomena. There is no work if mass or energy does not cross over higher or lower system boundary.[/quote]
In a closed system, no mass crosses the boundary of the system, but still, work can be done.
[quote]
Potential energy is not work, but change in potential energy is Work. Like wise 500ton metals at 500 deg. C does not have heat energy unless there exist a difference of temperature in system(500 ton metal) and surrounding.”
You are saying that heat cannot be transferred to a system unless there is a temperature gradient at the boundary, correct? Certainly, at the boundary, the temperature of the system must match the temperature of the surroundings (i.e., temperature is continuous at the boundary).
“Suppose that after we have compressed the piston, we release it. Intuitively, we would expect the piston to recoil back, and this is exactly what happens; the gas expands and does [an equal amount of] work on the piston against atmospheric pressure. ”
This is not quite correct. It is only correct if both the compression and expansion are done reversibly, which certainly is not the case if expansion occurs adiabatically against constant atmospheric pressure.
“That’s not the point I wanted to make. You don’t need external coils or the like for the Peltier effect. A heat flow may also be driven by purely mechanical forces without a temperature gradient. We know for more than 100 years by now (e.g. from the works of Pierre Curie in 1886) some basic principles of linear irreversible thermodynamics: General currents like heat current, mass current, electrical current, chemical reactions are driven by generalized forces like temperature gradients, pressure gradients, electrical potential gradients and chemical potential gradients. The important point is now that the linear relation between currents and forces is non-diagonal, i.e. in general, e.g. a pressure difference will not only drive a mass current but also a heat current ## \bf \rm even without the slightest temperature gradient. ##”
The corrected text is: Analysis on boundary, surrounding and system might clear out confusions. Both work and heat are boundary phenomena. There is no work if mass or energy does not cross over higher or lower system boundary. Potential energy is not work, but change in potential energy is work. Likewise, 500-ton metals at 500 deg. C do not have heat energy unless there exists a difference of temperature in the system (500-ton metal) and surrounding.