## Main Question or Discussion Point

I am a beginner in thermodynamics. I was going through a educational board's chapter on thermodynamics. I want to know if they are accurate and other comments if any. The statements are as below. Also we come across state variables in applications of current laws too. So what is special about state variables, how are they different from other variables.

1) The distinction between mechanics and thermodynamics is worth bearing in mind. In mechanics our interest is in the motion of particles or bodies under the action of forces and torques. Thermodynamics is not concerned with the motion of the system as a whole. It is concerned with the internal macroscopic state of the body. When a bullet is fired from a gun, what changes is the mechanical state of the bullet (its kinetic energy in particular), not its temperature. When the bullet pierces a wood and stops, the kinetic energy of the bullet gets converted into heat, changing the temperature of the bullet into the surrounding layers of wood. Temperature is related to the internal (disordered) motion of the bullet, not to the motion of the bullet as a whole.

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2) The concept of internal energy of a system is not difficult to understand. We know that every bulk system consists of a large number of molecules, internal energy is simply the sum of the kinetic energies and potential energies of these molecules. We remarked earlier that in thermodynamics the kinetic theory of the system as a whole, is not relevant. Internal energy is thus, is thus, the sum of molecular kinetic and potential energies in the frame of reference relative to which the centre of mass of the system is at rest. Thus, it includes only the (disordered) energy associated with the random motion of molecules of the system. We denote the internal energy of a system by U.

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3) The notion of heat should be carefully distinguished from the notion of internal energy. Heat is certainly energy, but it is the energy in transit. This is not just a play of words. The distinction is of basic significance. The state of a thermodynamic system is characterized by its internal energy, not heat. A statement like “a gas in a given state has a certain amount of heat” is as meaningless as the statement that “ a gas in a given state has a certain amount of work”. In contrast, “a gas in a given state has a certain amount of internal energy” is a perfectly meaningful statement. Similarly, the statements “ a certain amount of heat is supplied to the system’ or ‘ certain amount of work was done by the system’ are perfectly meaningful.

4) To summarise, heat and work in thermodynamics are not state variables. They are modes of energy transfer to a system resulting in change in internal energy, which as already mentioned is a state variable. For proper understanding of thermodynamics, however, the distinction between heat and internal energy is crucial.

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5) Now, the system may go from an initial state to the final state in a number of ways. Since internal energy is a state variable, delta(U) depends only on the initial and final sates and not on the path taken to go from initial and final states. However, delta(Q) and delta(W) will, in general, depend on the path taken to go from initial to final steates. From delta(Q) – delta(W) = delta(U), however, it is clear that the combination delta(Q) – delta(W) is, however, path independent.

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Danger
Gold Member
When a bullet is fired from a gun, what changes is the mechanical state of the bullet (its kinetic energy in particular), not its temperature. When the bullet pierces a wood and stops, the kinetic energy of the bullet gets converted into heat, changing the temperature of the bullet into the surrounding layers of wood.
While I don't know much about thermodynamics, I do know a bit about guns. The quoted statement is crap. A bullet absorbs tremendous heat from the combustion of the powder, and generates more through friction with the barrel on the way out. The impact does generate more for the aforementioned reasons, but it's not the only source of heat.

Andy Resnick
There's a lot here- let's break it down.

1) This is true, although the specific example is flawed as per Danger's observation. This is a key concept: thermodynamics does not require the existence of atoms to be correct, and leads to the next one:

2) I found the concept difficult to understand, but that's me. Remember, we don't need to resort to atoms to understand thermodynamics, so let's not even talk about them. I have come to understand the internal energy to be a 'configuration' energy. A chair within an empty room (with gravity) will have different internal energies depending on where the chair is- near the ceiling? On the floor? Is it intact or burned? Re-introducing atoms, a protein molecule will have different internal energies depending on it's configuration: folded, denatured, etc.

3) Yes- another key concept. Heat is the flux of energy.

4) I think this is true as well- I don't fully understand what a state variable is- other than the definition of a state variable being independent of path. I think the $$\DeltaPV$$ component of work (mechanical work) is a state variable.

5) That's true for equlibrium thermodynamics only, I think. I vaguely recall Jarzynski's equality pertaining to nonequilibrium thermodynamics...