Legendre Transformation: Find f(T,v)

[jesuslovesu]

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

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) ?

 

[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

 

[Zeppos10]

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.