Measure of the result of an adiabatic joule free expansion

Question

Response to the following problem:

(a) A measure of the result of an adiabatic Joule free expansion is provided by the louie coefficient η = (∂T/∂V)_{U .}

Show that η = - (1/C_V) ((βT/k) - P) .

(b) A measure of the result of the Joule-Thomson expansion (adiabatic throttling process or isenthalpic expansion) is provided by the Joule- Thomson coefficient  η = (∂T/∂P)_{H .}

Show that η = - V/C_P (βT - 1) .