Ideal gas temperature and 2nd law TD

[adichy]

Homework Statement

As an application of TD and to demonstrate the power of the formalism of differential forms,
show that if one defines the ideal gas temperature TI (T) from the ideal gas equation

p V = N K_B TI(T);

this is related to the absolute temperature T (from the second law) by
TI (T) ~ T

Homework Equations

the internal energy U=U(T)

dS= δQ / T

d²S/dVdT = d²S/dTdV

The Attempt at a Solution

I'm having difficulty on how to start the problem and what I'm supposed to be doing. Any direction will be appreciated. =)

thanks

 

[Mute]

What is "TD"? You should always define all acronyms you use, as you can't be sure they're common and everyone will know what you mean.

Since your problem talks about differential forms, you'll probably need to use something like the first law in the form $dU = \delta Q - p dV$, together with the other "relevant equations" you have.

 

[ChaseRLewis]

TD is thermodynamics

what is TI(T) though (Ideal temperature?) er... these are the same things (or have always been treated as such when I took graduate thermo) if T doesn't fit the model it's because the ideal model itself failed (reasonable since it has some big assumptions) so what ... they want you to make TI = T by showing for some set of assumptions TI = T? Most likely by using maxwell relationships (or formalism). just my guess.