Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 2.3-5

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · equations-of-state-entropy-representation

Problem

Find the three equations of state for a system with the fundamental relation

\frac{S}{R} = \frac{UV}{N} - \frac{N^3}{UV}

a

) Show that the equations of state in entropy representation are homogeneous zero-order functions.

b

) Show that the temperature is intrinsically positive.

c

) Find the ``mechanical equation of state''

P = P(T, v)

d

) Find the form of the adiabats in the

P

v

plane. (An ``adiabat'' is a locus of constant entropy, or an ``isentrope'').