Ideal gas temperature proportional to absolute temperature

[Joy Williams]

Homework Statement

I[/B] have some difficulties proving that the ideal gas temperature is directly proportional to absolute temperature defined by the second law of thermodynamics.

Homework Equations

The ideal gas temp. is defined by the ideal gas equation: pV=NkTi(T), where k is Boltzmann's constant and Ti(T) is the temp. of the ideal gas.

The Attempt at a Solution

The internal energy of the ideal gas is solely a function of the absolute temp.,U=U(T) and the that d^2S/dVdT=d^2S/dTdV.

 

[nilesh_pat]

Since the ideal gas equation is an expression of the second law of thermodynamics, we can conclude that the absolute temp. of the ideal gas is directly proportional to the ideal gas temp.