# Heat vs Thermal energy

There seems to be considerable confusion in the scientific community about thermal energy and heat. I have read several textbooks on thermodynamics and several posts in scientific forums and they certainly don't agree on what is heat and thermal energy. For some: thermal energy is the kinetic energy of the random motion of particles and heat is a transfer of energy between two body that are not in thermal equilibrium. For some thermal energy and heat are the same thing but they are a form of energy associated with the kinetic energy of the random motion of particles and not necessarily associated with transfer.

My questions are these:

Is there an actual agreement in the scientific community about these terms?

If there is, what is the most precise definition given to these terms? What is the mathematics behind it?

If there is not, what would be the most authoritative source that could be used to define them?

Do you know of any book that explain this thoroughly using even advanced mathematics and physics?

Thank you

## Answers and Replies

Andrew Mason
Science Advisor
Homework Helper
There seems to be considerable confusion in the scientific community about thermal energy and heat. I have read several textbooks on thermodynamics and several posts in scientific forums and they certainly don't agree on what is heat and thermal energy. For some: thermal energy is the kinetic energy of the random motion of particles and heat is a transfer of energy between two body that are not in thermal equilibrium. For some thermal energy and heat are the same thing but they are a form of energy associated with the kinetic energy of the random motion of particles and not necessarily associated with transfer.

My questions are these:

Is there an actual agreement in the scientific community about these terms?

If there is, what is the most precise definition given to these terms? What is the mathematics behind it?

If there is not, what would be the most authoritative source that could be used to define them?

Do you know of any book that explain this thoroughly using even advanced mathematics and physics?

Thank you
There is general agreement that $\Delta Q$ is "heat flow". But, apart from that, "heat" is a loose term that can be used to refer to different things. The confusing use of the term "heat" may be historical. Heat was originally thought to be some kind of substance that flowed between bodies.

"Heat flow" is embodied in the first law of thermodynamics:

$$\Delta Q = \Delta U + W$$

When applying the first law to a thermodynamic process involving a system, $\Delta Q$ is the heat that flows into the system during the process, $\Delta U$ is the change in internal energy of the system, and W is the work done by the system. If the heat flow is into the system, $\Delta Q$ is positive. If the heat flow is out of the system, $\Delta Q$ is negative. Sometimes scientists use the term "heat" to mean $\Delta Q$.

"Heat" is often used in a different context - as something that a body contains - ie. the quantity of "heat" contained by a body. This is not a good idea to use heat in this way because it causes confusion with $\Delta Q$.

$\Delta Q$ does not refer to anything "contained" by a body. It refers to energy transfer to or from the system during a process. W - work - does not refer to anything contained by a body either. W refers to the mechanical work that is performed by the system during a process. In the first law, the only quantity that represents to something contained by a body is $\Delta U$ - the internal energy of the system.

AM

Last edited:
Thank you very much for your answer.
It seems clear to me now that heat is energy in transfer. What is thermal energy? Is it the same as heat? If a bullet is stopped suddenly, what energy transfer is taking place since it cannot be heat?
Regards,

Andrew Mason
Science Advisor
Homework Helper
Thank you very much for your answer.
It seems clear to me now that heat is energy in transfer. What is thermal energy? Is it the same as heat? If a bullet is stopped suddenly, what energy transfer is taking place since it cannot be heat?
Regards,
Thermal energy a form of internal energy. It is the energy due to the kinetic energy of the molecules in a substance which is in thermal equilibrium (ie in which the molecular kinetic energies follow a Maxwell-Boltzmann distribution).

A bullet stopping in a piece of wood is an example of Work: a force being applied through a distance. In that case, the work being done on the wood increases its internal energy. Since dQ = 0, dU = dW (first law of thermodynamics).

AM