Determine the region of moderate pressures

Question

Response to the following problem:

(a) Show that in a Joule-Thomson expansion, no temperature change occurs if  (∂v/∂T)_P = v/T

(b) Show that μc_P = T((∂v/∂T)_P -v

In the region of moderate pressures, the equation of state of 1mol of gas may be written

Pv = RT + B’P + C’P²  ,

where the second and third virial coefficients B and C are functions of T only. (c) Show that, as the pressure approaches zero,

μc_P → T(dB’/dT) - B’

(d) Show that the equation of the inversion curve is P = B’ -T(dB’/dT)/C’ - T(dC’/dT) .