Legendre Transformation: Find f(T,v)

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SUMMARY

The discussion focuses on deriving the Legendre transformation for the function f(T,v) from the thermodynamic identity du = T ds - p dv. The user attempts to express f(T,v) in terms of internal energy U(T) and pressure P(v), ultimately suggesting that the result should lead to the enthalpy H. The conversation highlights the importance of understanding thermodynamic potentials and their differential forms, confirming that the Legendre transformation is a critical tool in thermodynamics.

PREREQUISITES
  • Understanding of thermodynamic identities, specifically du = T ds - p dv.
  • Familiarity with Legendre transformations in thermodynamics.
  • Knowledge of thermodynamic potentials, including internal energy and enthalpy.
  • Basic calculus, particularly partial derivatives and differential forms.
NEXT STEPS
  • Study the derivation of Legendre transformations in thermodynamics.
  • Explore the relationship between internal energy U(T) and enthalpy H.
  • Review differential forms of thermodynamic potentials.
  • Investigate the thread 'Why Legendre Transform' on Physics Forums for additional insights.
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying or working with thermodynamic potentials and transformations, will benefit from this discussion.

jesuslovesu
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Homework Statement



du = T ds - p dv

Find a Legendre transformation giving f(T,v)

The Attempt at a Solution


Can anyone check if this is remotely correct?

f(T,v)
[tex]df = \partial f/\partial T dT + \partial f/\partial v dv[/tex]

du = Tds - p dv
u = f - vp
d(f-vp) = Tds + v dp - p dv - v dp
df = Tds - pdv
f(T,v) = U(T) -P(v) ?
 
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I'm not sure about the work but these are thermodynamic potentials you're working with, the one given is the internal energy, and if you scroll about halfway down to see them in differential form you'll see you should end up with H, enthalpy. Should give you something else to look for, I don't have my thermo book on me but it worked out those transforms
 
jesuslovesu said:

Homework Statement



du = T ds - p dv
Find a Legendre transformation giving f(T,v)

Allthough its rather late in the day to answer this question, you may want to look at the thread called 'why Legendre Transform' in physicsforums.
 

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