Entropy And Energy Representation

[hurz]

How do I go from the entropy of a system, S(U,V,N), to its internal energy, U(S,V,N)?
For instance, for an ideal classical gas, we have

S=(3/2)N*R*ln(U/N) + N*R(V/N) + N*R*c

where R is the Boltzmann constant, N is the particle number, V is the volume and "c" is a constant.

How can I convert this to U(S,V,N) ?

The unswer is U=N*(U/N)^(2/3)*exp[(2/3)*(S/(N*R)-c)]

Regards,
hurz.

 

[mfb]

This is just algebra. Isolate ln(U/N), use e^() on both sides and multiply with N.

 

[hurz]

my bad. thanks!