[Hushai]

What is the most accurate and complete definition of heat in thermodynamics?
Is there a mathematical explanation distinguishing between work and heat? 

 A fellow teacher gave me this example:

"Imagine a thin box containing two gases below room temperature.  The gases are divided by a removable shield.  When the shield is removed the gases can mix and create a spontaneous exothermic reaction.  If this reaction initiates while the temperatures of both gases are still below room temperature (temperature of the surroundings), the heat generated will cause the temperature of the system to increase above the temperature of the surroundings before heat is given off by the system to the surroundings, yet it is still an exothermic reaction.  I'm not sure what you could define as the system other than the gases inside the box that would make sense.  In any case, the system would have to be heated up before the surroundings if it starts at a lower temperature than the surroundings.  This wouldn't alter the definition of an exothermic reaction."

I like this example but it still causes me a problem.  The system has clearly been defined and heat has been generated inside the system before there is any transfer.   Or heat is defined as  a  transfer of energy between two systems.  So can we still talk about heat?  Shouldn't we rather talk about increased kinetic energy of the random motion of particles?

It looks to me like we cannot avoid defining heat as simply the kinetic energy of the random motion of the particles.  Work would be the average force applied on particles * average velocity of particles.  Heat would be the work associated with the random fluctuation of forces and velocites of the particles.

I am just trying to understand.

Thank you

[DevaDevil]

I would define heat as a difference in thermal energy between two separate systems, which can cause a flux. In your case, the difference in thermal energy between the gases and the surroundings.

In the first state, the gases are at a lower temperature (lower thermal energy) than the surroundings, so there will be energy transfer from surroundings to gases, a.k.a. heat flux from surroundings to gases; or better defined: heat flux into the system. (with the system defined as the vessel with the gases)

At the end state, the gases will have a higher temperature than the surroundings due to the reaction energy, thus causing a heat flux from gases to surroundings, or: heat flux out of the system.


IF you assume the system (the gases) to be at constant pressure, then compared to the first state, the system will donate energy to the surroundings, thus making the reaction defined to be exothermic. Usually a better way to determine the endo- or exothermicity of the reaction is to look at the reaction enthalpy. If that is negative, then we call it a exothermic reaction, regardless of the heat flux at that moment.

Maybe someone more specialized in thermodynamics can give a more accurate definition, but I find this workable for me.

[vmelkon]

I like this example but it still causes me a problem.  The system has clearly been defined and heat has been generated inside the system before there is any transfer.   Or heat is defined as  a  transfer of energy between two systems.  So can we still talk about heat?  Shouldn't we rather talk about increased kinetic energy of the random motion of particles?

I'm not into thermodynamics.

I would not describe heat as "a transfer of energy between two systems".
I would define it as kinetic movement of atoms or molecules. I would also define it as rotation of the molecule. Rotation of subgroups on the molecule.

I think that it is somewhat an ill-defined term because it doesn't tell us what exactly the molecule is doing. All we know is that you insert a mercury thermometer into a system and it goes to 20 C. If we insert some other type of thermometer, it shows 20 C.
But are the mercury atoms and the atoms in the system at the same energy level? Are the molecules of the second thermometer in the same state as the system?

To me it seems heat is a rather classical concept.

[rabolisk]

The best definition of heat I can find is from an article in Physics Education

Heat is "energy in the process of being transferred due to a difference in temperature"

http://iopscience.iop.org/0031-9120/35/5/301/pdf/0031-9120_35_5_301.pdf

To me, a fundamental property of heat is that it is not a state function. It is wrong to say that a system "contains" heat. Heat does not describe the state of the system in anyway. Heat is related to a PROCESS or transfer. There are other definitions of heat, especially those that invoke entropy. Regardless, even if I can't correctly describe heat in the most general and formal terms, I know what is incorrect, and that would be suggesting that heat is simply the kinetic energy of the random motion of molecules.

[Hushai]

Thank you