Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 3.4-12

SOME FORMAL RELATIONSHIPS, AND SAMPLE SYSTEMS

Physics — Statistical Mechanics · electrochemical-potential-ideal-gas

Problem

Show that

\mu_j

, the electrochemical potential of the

j

th component in a multicomponent simple ideal gas, satisfies

\mu_j = RT\ln\left(\frac{N_j v_0}{V}\right) + (\text{function of } T)

and find the explicit form of the ``function of

T

.'' Show that

\mu_j

can be expressed in terms of the ``partial pressure'' (Problem 3.4-11) and the temperature.