How to Convert Cp to Cv for Metals?

[Walkingman]

Can someone please remind me how to convert values of Heat capacaty at constant pressure to heat capacity at constant volume? I believe it has something to do with the volume expansivity (1/V)*(dV/dT) at constant pressure, but I can't find my therm textbook and I can't remember how to proceed.

 

[mezarashi]

Here are some useful relations:

$$\frac{du}{dT}= C_v (T)$$

$$\frac{dh}{dT}= C_p (T)$$

$$h = u + Pv$$

 

[mezarashi]

On second note, using those equations to solve, the math turns out to be more challenging than I thought, although I remember it can be done.

I found a chapter summary from McGrawHill that has an excellent example. See pages 14 and 15.

http://highered.mcgraw-hill.com/sites/dl/free/0072383321/22366/study_guide_ch11.pdf

 

[Walkingman]

Thanks, that link helped!