Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 1.8-6

THE CONDITIONS OF EQUILIBRIUM

Physics — Statistical Mechanics · energy-from-equations-of-state

Problem

For a particular system it is found that if the volume is kept constant at the value

V_0

and the pressure is changed from

P_0

to an arbitrary pressure

P'

, the heat transfer to the system is

Q' = A(P' - P_0) \qquad (A > 0)

In addition it is known that the adiabats of the system are of the form

PV^\gamma = \text{constant} \quad (\gamma \text{ a positive constant})

Find the energy

U(P,V)

for an arbitrary point in the

P

–

V

plane, expressing

U(P,V)

in terms of

P_0

V_0

A

U_0 \equiv U(P_0, V_0)

and

\gamma

(as well as

P

and

V