Help me to solve the equation from Thermodynamics

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The discussion revolves around deriving the equation Cp - Cv = T(dP/dT)v * (dV/dT)p in thermodynamics, with participants seeking clarification on the variables involved and the equations needed for the derivation. The original poster indicates that this is an assignment given by their lecturer without sufficient details. There is a request for more information on how to express changes in internal energy (dU) in terms of entropy (dS) and volume (dV), as well as how to represent entropy as a function of temperature and pressure. The conversation emphasizes the need for a clearer understanding of the underlying concepts and equations to successfully complete the assignment. Overall, the thread highlights the challenges students face when tackling complex thermodynamic equations without adequate guidance.
Adib Morzuki
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Someone can help me to prove the question below please!

someone know how to derive this equation Cp-Cv=T(dP/dT)v*(dV/dT)p*?
 
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You need to say what all those variables represent, and what equation(s) you have from which you wish to derive this one. What is the actual full question you are trying to answer?
 
This sounds like a homework problem. Is it?
 
mal4mac said:
You need to say what all those variables represent, and what equation(s) you have from which you wish to derive this one. What is the actual full question you are trying to answer?
That is the problem. My lecturer asked me to derive the equation given without any details.
 
Chestermiller said:
This sounds like a homework problem. Is it?
More like it but it is an assignment for us. My lecturer just gave us that equation and asked to derive the equation without any details.
 
*UPDATE*

The question are asking how to prove the left equation equal to the right equation
 
What is dU in terms of dS and dV? If we represent the entropy S as S(T,P), what is dS in terms of the partial derivatives of S with respect to T , P, and dT and dP?

Chet