Any residual property is defined to be where IG denotes the same property in the ideal

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Any residual property θ is defined to be

res (T, P) = 0 (T, P) - 0G (T, P)

where IG denotes the same property in the ideal gas state. Such a quantity is also referred to as a departure function.

a. Develop general expressions for dHres, dUres, dSres, and dGres with temperature and pressure as the independent variables. 

b. Recognizing that as P → 0 all fluids become ideal gases, so that their residual properties are zero, develop explicit expressions for the residual properties Hres, Ures, Sres, and Gres as functions of temperature and pressure for the van der Waals equation of state. 

c. Repeat part (a) for the Peng-Robinson equation of state.

P = RT aa Vm-b V2+2bVm  b 

d. Repeat part (a) for the Redlich-Kwong equation of state.

Problems Involving the Redlich-Kwong Equation of State (6.35–6.48).

P = RT V-b a(T) V(V+b) (6.4-1b)

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