Thermodynamics: Internal Pressure calculus

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SUMMARY

The forum discussion centers on the calculation of internal pressure in thermodynamics, specifically relating to the internal energy equation U = U(S,V). A first-year undergraduate expresses confusion about the mathematical derivation of this result and seeks clarification. The response emphasizes the necessity of understanding partial differential equations to grasp the concepts of thermodynamics effectively.

PREREQUISITES
  • Understanding of thermodynamic principles, particularly internal energy.
  • Familiarity with the equation U = U(S,V) and its implications.
  • Knowledge of partial differential equations and their application in thermodynamics.
  • Basic mathematical skills relevant to calculus and thermodynamic equations.
NEXT STEPS
  • Study the fundamentals of partial differential equations and their role in thermodynamics.
  • Research the derivation of internal energy equations in thermodynamic contexts.
  • Explore advanced thermodynamic concepts, including Maxwell's relations.
  • Review mathematical techniques used in thermodynamic calculations, such as the chain rule.
USEFUL FOR

This discussion is beneficial for first-year undergraduate students in physics or engineering, educators teaching thermodynamics, and anyone seeking to deepen their understanding of internal energy and its mathematical foundations.

thesidjway
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I'm extremely sorry for not using the template. One of my thermodynamics instructors used this relation to prove another result. I know what to do next and the other steps to end up at the final result but I don't know how this result came.
Is it simply mathematics that I'm not aware of, or is this a standard result? In both cases, kindly help me out! I'm stuck

[PLAIN]https://thesidjway.files.wordpress.com/2014/08/kaise.jpg[/IMG

Thanks in Advance
(I'm a first year undergraduate)
 
Last edited by a moderator:
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thesidjway said:
kaise.jpg
The internal energy U was expressed as U = U (S,V). Have you had anything in your courses on partial differential equations yet? If not, you are going to have big trouble understanding this development as well as all the rest of thermodynamics. Sorry for the bad news.

Chet
 

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