Suppose we have a stationary billiards ball. Roll a cue ball so it hits the billiards ball, and the billiards ball starts moving. We would say that the cue ball does work on the billiards ball. That work can be calculated from the forces and displacements during the collision. If our collision is perfectly elastic, then presumably all the energy transferred it transferred via work.

Now suppose one gas molecule collides with another. This situation would seem to be the same; there's an elastic collision; energy should be transferred as work.

But now suppose there is a whole room full of heavy cold gas on bottom and light warm gas on top. Now we would say that heat flows through the gases via conduction, entropy is generated, etc. But at no point is there any physical process besides simply a collision between molecules. If the energy transfer is just a bunch of intermolecular collisions, each of which transfers energy via work, why is energy transferred via heat from the macroscopic perspective?

If all the above is correct, it would seem there is some sort of transition where as the number of molecules increases, energy transfer changes from work to heat, or else with some change of perspective from a microscopic to macroscopic description the energy transfer changes from work to heat. But in that case, why should things like the second law of thermodynamics depend on your choice of perspective, or the number of molecules in your system?


1 Answer 1


You are right in saying it is a change of perspective: Heat isn't really a useful concept for small systems. Heat is only really used to describe big systems where it is impossible to keep track of individual kinetic energies of particles. The transition between talking about kinetic energies to heat just depends on how we want to describe the system.

Entropy isn't subjective though, check out this thread: Is amount of entropy subjective?

The take away message is that when you describe a system w.r.t a set of parameters, entropy will be an objective function of those parameters, but may be different depending on what parameters are chosen. In the thermodynamic limit, we typically talk about a system in terms of its temperature, or heat possessed etc. but for smaller systems, we will often know about each individual particle's position/momentum. Entropy is the uncertainty of the systems internal state for the given parameters. So if we specify a system in terms of all of its physical degrees of freedom, its entropy will be zero (though this is infeasible for large systems).

The second law then applies to the entropy for the parameters chosen and will always stay the same or increase. (but any interactions the system undergoes must be describable with these parameters!).

As an example, Consider a system of two volumes of gas at different temperatures. We then bring them in thermal contact: If we describe the system in terms of temperatures and pressures of the two subsystems, entropy of the system will increase. (heat flow across different temperatures is irreversible) Whereas if we knew the positions and momentum of all of the gas molecules, the entropy would not change in this process. Although we will never know this in practice, neither of these descriptions violates the second law.

The significance of the second law is that unless your parameters can completely describe your systems internal state, the entropy of the description will increase over time.


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