# Thermodynamics - calculate entropy

1. May 4, 2004

### alpha_wolf

Hi.

I need to calculate the entropy of some material at a certain temperature given the Cp at each phase and the entalpy change and temperature at phase transitions. I'm supposed to use thermodynamic considerations (i.e. statistical definition of entropy is not applicable/allowed).

I know how to translate the entalpy change to entropy change, so I was thinking of doing an itegral of (Cp/T)dT across each of the temperature ranges, and then summing up the intergals and the entropy changes of the phase transitions. The problem is that the first integral is from 0K to the first transition temperature, so it gives ln(0) as one of the components. This is obviously not usable... I suppose this is because the polynomial definition for Cp breaks down at extremely low temperatures.

How can I overcome the problem? Maybe assume the entropy change near absolute zero is negligible and integrate from 0.1K instead of 0K? The numbers don't quite agree with that assumption...

Last edited: May 4, 2004
2. May 4, 2004

### Bystander

Yeah --- if you're doing third law entropies. Standard entropies give you a little wiggle room --- standard entropies of formation of elements are defined to be zero at standard conditions; compounds have non-zero entropies of formation, but they have been measured for a limited set of cases. Yours may be among them.

Third law? You've run into Einstein and Debye models for heat capacity at absolute zero? No problem integrating from zero.

3. May 4, 2004

### alpha_wolf

The material in my case is pure zinc. The question doesn't state anything about standard anything, and the chapter is about the third law, so I'm assuming they want third law entropy. Perhaps there's a way to combine third law and standard entropies somehow?

Cp for the first phase is given as A + BT, where A and B are constants. An integral of Cp/T thus gives A*ln(T1) as one of the components, and when T1=0, that is a problem. I don't think we have encountered Einstein and Debye, but perhaps I just don't recognise the name of the model... Can you remind me please?

4. May 5, 2004

### Bystander

Third law S: 0 at 0 K. Standard state: 0 at 298 K. No combination. Hit the library for Ch. 6 in Lewis & Randall, or beat up your text index for Debye, Born and von Karman, Dewar, Einstein, Dulong & Petit (the failure at low T), Nernst.

No stat allowed? This really gets into a gray area --- D. and B. & vK. are not exactly "classical" derivations of the functional form of heat capacity at low T.