1. The problem statement, all variables and given/known data I have some difficulties proving that the ideal gas temperature is directly proportional to absolute temperature defined by the second law of thermodynamics. 2. Relevant 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. 3. 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.