Legendre Equation

1. Jan 3, 2008

jesuslovesu

1. The problem statement, all variables and given/known data

du = T ds - p dv

Find a Legendre transformation giving f(T,v)

3. The attempt at a solution
Can anyone check if this is remotely correct?

f(T,v)
$$df = \partial f/\partial T dT + \partial f/\partial v dv$$

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) ?

Last edited: Jan 3, 2008
2. Jan 3, 2008

blochwave

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

3. Dec 21, 2009

Zeppos10

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.