2) Using the equations dH=TdS+VdP and dG=-TdS+VdP a) Show that (dH/dP) T = -TV(b

Question

2) Using the equations dH=TdS+VdP and dG=-TdS+VdP

a) Show that (dH/dP)T = -TV(beta)+V where beta = 1/V * (dV/dT)p

b) Calculate (dH/dP)T for 1 mole of an ideal gas and for 1 mole of a Clausius gas that obeys the equation of state P(V-nb) = nRT where b =38.6*10-6 m3mol-1

c) Using the equations dU=TdS+PdV and dA=-TdS+PdV show that (dU/dV)T=T(beta)/(kappa) -P where beta=1/V * (dV/dT)P and kappa = -1/V * (dV/dP)T

d) Calculate (dU/dV)T for an ideal gas and for a gas that obeys that van der Waals equation of state (P+an2/V2)(V-nb)=nRT. Assume n=1, V=1m3 and a = 1.35*10-6m6bar*mol-2.

Hint: For working this problem you will find the following relationship useful:

(dV/dP)T(dP/dT)V(dT/dV)p=-1

Am in need of some serious help here.

Explanation / Answer

2) Using the equations dH=TdS+VdP and dG=-TdS+VdP a) Show that (dH/dP) T = -TV(b

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