Suppose a gas has an ideal gas heat capacity of CP=(7/2)R and is described by the equation of state: Z = 1 + (CP2)/(RT) With C = 100 cm3/bar-mol. (R=83.14 bar-cm3/mol-K)

Question

A) Find a general expression for the enthalpy departure function for this gas.
B) Find a general expression for the entropy departure function for this gas.
C) Find ?H and ?S for the gas if it is isothermally compressed from P=1 bar and T=400 K to P=50 bar and T=400 K.
Note: To receive full credit on A and B, your answers should be ALGEBRAIC expressions in terms of MEASUREABLE properties and/or known constants; all derivatives and integrals must be evaluated.

Answer 1

Apply definition of residual enthalpy for a gas, integrating with respect to dP:



Substitute ?V and ((??V)/?T)_P into ?H^Requation all in terms of C, P, and T:



Apply definition of residual entropy of gas, integrating with respect to dP:



Total change in enthalpy for gas:



(Where ?H_1^R could also be assumed to be negligible due to ideal gas behavior @ P = 1 bar)

Evaluate ?H_2^R:





This result demonstrates an assumption that ?H_1^R~0 is justified.

?H_2^ig-?H_1^ig, the change in enthalpy for the ideal gas, is 0, since H is only a function of temperature for an ideal gas and the process is isothermal. Plug residual enthalpy terms into change in enthalpy equation:



Total change in entropy for gas:



Where ?S_1^Rand ?S_2^R are both 0 as derived previously

Evaluate ?S_2^ig-?S_1^ig:



Substitute into change in entropy equation: