Thermodynamic derivation of heat capacity

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SUMMARY

The discussion focuses on the thermodynamic derivation of heat capacity, specifically the relationship between heat capacities at constant pressure (cp) and constant volume (cv). The equation cp = cv + TV(∂P/∂T)V is referenced, along with the Maxwell relations and the fundamental thermodynamic equation TdS = dU + PdV. Participants express uncertainty in applying these equations, particularly in the context of ideal gases.

PREREQUISITES
  • Understanding of thermodynamic principles, particularly heat capacities.
  • Familiarity with Maxwell relations in thermodynamics.
  • Knowledge of the fundamental thermodynamic equation TdS = dU + PdV.
  • Basic concepts of ideal gas behavior.
NEXT STEPS
  • Study the derivation of cp and cv for ideal gases.
  • Explore the application of Maxwell relations in thermodynamic calculations.
  • Learn about the implications of the equation cp = cv + TV(∂P/∂T)V.
  • Investigate the relationship between entropy (S) and temperature (T) in thermodynamics.
USEFUL FOR

Students and professionals in physics and engineering, particularly those specializing in thermodynamics and heat transfer.

tarletontexan
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Homework Statement



cp=cv+TV?^2/?

Homework Equations




cp=T/N(\partialS/\partialT)p

The Attempt at a Solution


I have the equation, just not sure how to apply it? Any help would be appreciated
 
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tarletontexan said:

Homework Statement



cp=cv+TV?^2/?

Homework Equations




cp=T/N(\partialS/\partialT)p

The Attempt at a Solution


I have the equation, just not sure how to apply it? Any help would be appreciated

I am not sure what the question is. Are we dealing with an ideal gas?

AM
 
yes, I know that there are several maxwell relations to get to the solution I just don't know how to apply them.
 
tarletontexan said:
yes, I know that there are several maxwell relations to get to the solution I just don't know how to apply them.
Start with:

TdS = dU + PdV

CP = (∂Q/∂T)P = T(∂S/∂T)P = (∂U/∂T)P + P(∂V/∂T)P

AM
 

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