Heat Capacity

[John Malcolm]

I understand that as a result of the 3rd Law of Thermodynamics the heat capacity of a substance approaches zero as the absolute temperature approaches zero. What happens to the heat capacity as temperature approaches infinity?

[dalemiller]

I understand that as a result of the 3rd Law of Thermodynamics the heat capacity of a substance approaches zero as the absolute temperature approaches zero. What happens to the heat capacity as temperature approaches infinity?

Is that infinity F or infinity C? But wouldn't something's molecules wiggle at c before it could get quite so hot? By then it would be somewhere else far away.

[timo]

I can't think of anything special happening. Mayhaps you'd approach the heat capacity of an ideal gas; assuming free practically non-interacting particles for [math]T\to \infty[/math] doesn't sound like the worst be to me (especially when no actual setup is provided).

 

@Dalemiller: The letter you use to describe it is completely irrelevant. What's meant is the heat capacity, irrespective of whether volume of pressure is held constant. The background is that at zero temperature a tiny increase in energy can provide a significant increase in temperature, formally being a heat capacity of "infinity" (huh, sounds very scientific, doesn't it?). There's also no limit on temperature and the assumption that on some finite temperature the object's molecules "wiggle at c" is problematic (i.e. wrong) for several reasons, the simplest being that a molecule cannot move at c in the first place.

[swansont]

Is that infinity F or infinity C?

 

For finite values they are different by ~ a factor of two. But as they approach infinity, that doesn't matter - it's the same limit.

[timo]

For finite values they [F and C] are different by ~ a factor of two. But as they approach infinity, that doesn't matter - it's the same limit.

What's "F" and "C", by the way? The standard thermo cryptography I know defines F as the free energy but I don't see how this would make sense in this context (where a natural choice seems to be F=0 for T=0).

[swansont]

What's "F" and "C", by the way? The standard thermo cryptography I know defines F as the free energy but I don't see how this would make sense in this context (where a natural choice seems to be F=0 for T=0).

 

I was assuming Fahrenheit and Celsius.