Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 3.4-2

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · ideal-gas-adiabatic-compression

Problem

Show that the relation between the volume and the pressure of a monatomic ideal gas undergoing a quasi-static adiabatic compression (

dQ = T\,dS = 0

S =

constant) is

Pv^{5/3} = \left(P_0 v_0^{5/3} e^{-2s_0/3R}\right)e^{2s/3R} = \text{constant}

Sketch a family of such ``adiabats'' in a graph of

P

versus

V

. Find the corresponding relation for a simple ideal gas.