Thermodynamic derivation involving heat capacitiesby mcdonkdik Tags: chemical engineering, maxwell relations, thermodynamics 

#1
Oct511, 06:22 AM

P: 4

I have the answer to this question but I'm finding it hard making sense of it...
Q5) Dervive a relationship relating C_{p}C_{v} to the isothermal compressibility (∂p/∂V)_{T} and the coefficient of thermal expansion (∂V/∂T)_{p}. Hint: consider the intensive entropy S as a function of T and V. So I've started with S(T, V): dS = (∂S/∂T)dT + (∂S/∂V)dV Apparently we take the partial derivative wrt T while holding p(pressure) constant.. then we use a Maxwell relation to remove the partial derivative containing S. Then we use the triple product rule for something. We end up with: C_{p}  C_{v} = T(∂p/∂V)_{T}(∂V/∂T)^{2}_{p} I'd really appreciate it if someone could give me a thorough explanation of how to do this. Many thanks! 



#2
Oct511, 11:14 AM

Sci Advisor
HW Helper
PF Gold
P: 2,532

Hi mcdonkdik, welcome to PF. Nobody's going to solve your problem for you, but if you work through the recommended steps (which constitute the entire solution already!) and show where you get hung up, you'll likely get helpful comments.




#3
Oct511, 12:36 PM

P: 4

Thnx 


Register to reply 
Related Discussions  
Heat capacities of a gas mixture.  Introductory Physics Homework  1  
Calculating the ratio between heat capacities of a gas  Classical Physics  4  
Molar Heat Capacities. Help?  Introductory Physics Homework  11  
heat capacities  Introductory Physics Homework  5  
Specific Heat Capacities/Latent Heat  Introductory Physics Homework  13 