What Is Heat? The Real Thermodynamics Definition Explained
Heat is not something a body possesses. Heat is a transfer mechanism: the non-mechanical exchange of energy between a system and its surroundings that occurs because of a temperature difference. A body has internal energy; it does not “have heat.” This distinction matters because the first law of thermodynamics, ΔU = Q + W, treats heat (Q) and work (W) as two separate modes of energy transfer, not as properties stored inside an object.
Table of Contents
Key Takeaways
- The first law of thermodynamics is written as ΔU = Q + W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done on the system.
- Internal energy is a state function made up of translational kinetic energy, rotational kinetic energy, vibrational kinetic energy, and intermolecular potential energy.
- Two identical gas cylinders starting at 373 K and ending at 473 K with matching pressure, volume, and temperature are indistinguishable afterward, even if one reached that state by compression (work) and the other by heating (heat).
- Heat is formally defined as the non-mechanical exchange of energy between a system and its surroundings caused by a temperature difference.
- Some texts reserve the term “thermal energy” for only the translational kinetic contribution to internal energy, which can create confusion if not explicitly defined.
What Does the First Law of Thermodynamics Actually State?
The first law of thermodynamics is a statement of the principle of conservation of energy. It is commonly written as:
ΔU = Q + W
In this equation, ΔU represents the change in a system’s internal energy, Q represents heat added to the system, and W represents work done on the system. The sign convention treats work done on the system as positive and heat added to the system as positive, so both terms contribute directly to raising internal energy.
What Is Internal Energy?
Internal energy is the energy associated with the microscopic degrees of freedom of a system, meaning the random motion and interactions of the molecules that make it up. For a general fluid, internal energy is the sum of four microscopic contributions:
- Translational kinetic energy of molecules
- Rotational kinetic energy
- Vibrational kinetic energy
- Intermolecular potential energy
Internal energy is a state function, meaning the change in internal energy between any two equilibrium states is independent of the path taken to get there. Because of this, it is technically incorrect to describe internal energy as “heat.” Heat describes a transfer mechanism between a system and its surroundings, not a quantity a body holds onto.
What Counts as Work in Thermodynamics?
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 inside a cylinder, where the external agent doing the pushing performs work on the gas.
Under the standard sign convention, work done on the system is positive. If a gas expands and pushes a piston outward instead, the gas does work on its surroundings and W becomes negative. If the cylinder walls are adiabatic, meaning no heat transfer occurs through them, then all work done on the gas goes directly into increasing its internal energy.
How Is Heat Different From Temperature and Internal Energy?
Temperature provides a useful bridge between microscopic motion and macroscopic observation. A kinetic definition of temperature treats it as a measure of the average translational kinetic energy of the particles in a system. Temperature and internal energy are related, but they are not simply proportional in general, because internal energy also includes rotational, vibrational, and potential energy contributions that temperature alone does not capture.
A system’s internal energy can be increased in one of two ways: by doing work on it, or by adding heat to it. These two paths can produce results that are experimentally indistinguishable from each other once the process is complete.
Why Can’t You Tell Whether Energy Was Added as Heat or Work?
Consider two identical cylinders of gas, both starting at 373 K. Compress one cylinder, delivering energy as work. Heat the other cylinder, delivering energy as heat. If both cylinders end up at 473 K with identical macroscopic properties, meaning matching pressure, volume, and temperature, their final states are indistinguishable.
No experiment performed on the final states alone can determine which cylinder was compressed and which was heated. Both cylinders simply show an increase in internal energy. This thought experiment demonstrates that heat and work are both modes of energy transfer between a system and its surroundings, not properties contained within the system itself.
What Is the 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 rather than stored quantities, the common phrase “a body possesses heat” is misleading.
It is more accurate to say a body has internal energy, or that energy has been transferred to a body by heat. Likewise, instead of saying “a body’s heat has increased,” the technically correct phrasing is “the body’s internal energy has increased” or “the body has gained energy by heat.”
Glossary
- Internal energy (U): the total energy associated with a system’s microscopic degrees of freedom, including translational, rotational, vibrational, and intermolecular potential energy.
- Heat (Q): the non-mechanical transfer of energy between a system and its surroundings caused by a temperature difference.
- Work (W): macroscopic energy transfer that occurs via a generalized force acting through a displacement.
- State function: a property whose change between two equilibrium states depends only on those states, not on the path taken between them.
- Adiabatic: describing a process or boundary through which no heat transfer occurs.
- Thermal energy: a term some texts use specifically for the translational kinetic contribution to internal energy; usage varies by source.
Frequently Asked Questions
Is it correct to say a hot object “has a lot of heat”?
No. Heat describes a transfer of energy between a system and its surroundings due to a temperature difference, not a quantity stored inside an object. A hot object has a large amount of internal energy. The correct phrasing is that energy has been transferred to the object by heat, not that the object contains heat.
What is the difference between heat and internal energy?
Internal energy is a state function representing the total microscopic energy of a system, including translational, rotational, vibrational, and intermolecular potential contributions. Heat is one of two mechanisms, alongside work, by which internal energy can change. Internal energy is a property of the system; heat is a process occurring at its boundary.
Can you tell whether a system was heated or had work done on it just by examining its final state?
No. If two identical systems reach the same final pressure, volume, and temperature, their macroscopic properties will be indistinguishable regardless of whether the energy arrived as heat or as work. Only the process history, not the final equilibrium state, reveals which transfer mechanism was used.
What is the first law of thermodynamics in equation form?
The first law is commonly written as ΔU = Q + W, where ΔU is the change in internal energy, Q is heat added to the system, and W is work done on the system. Under this sign convention, both heat added and work done on the system increase internal energy.
Why does internal energy include more than just temperature-related motion?
Temperature reflects the average translational kinetic energy of particles in a system, but internal energy also includes rotational kinetic energy, vibrational kinetic energy, and intermolecular potential energy. Because of these additional contributions, internal energy and temperature are related but not simply proportional in general.
Further Reading
- Finn, C. B. P., Thermal Physics, 2nd Edition.
- Heat — HyperPhysics
- Internal Energy — HyperPhysics
- Forum discussion on defining heat
- Thermodynamics basics overview
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.