Help me to solve the equation from Thermodynamics

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SUMMARY

The discussion centers on deriving the thermodynamic equation Cp - Cv = T(dP/dT)v * (dV/dT)p. Participants emphasize the need to clarify the variables involved, including Cp (heat capacity at constant pressure), Cv (heat capacity at constant volume), T (temperature), P (pressure), and V (volume). The conversation highlights the importance of understanding the relationships between these variables and the fundamental equations of thermodynamics, particularly in the context of an assignment given by a lecturer.

PREREQUISITES
  • Understanding of thermodynamic concepts such as heat capacities (Cp and Cv)
  • Familiarity with partial derivatives in thermodynamics
  • Knowledge of the first law of thermodynamics
  • Ability to interpret thermodynamic equations and variables
NEXT STEPS
  • Study the derivation of the first law of thermodynamics
  • Learn about the Maxwell relations in thermodynamics
  • Explore the relationship between entropy (S), temperature (T), and pressure (P)
  • Investigate the implications of heat capacities in different thermodynamic processes
USEFUL FOR

Students of thermodynamics, particularly those tackling assignments or exams involving the derivation of thermodynamic equations, as well as educators seeking to clarify these concepts for their students.

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*?
 
Last edited:
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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
 

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