Residual Properties by Equations of State

Residual Properties from the Virial Equations of State 

Evaluation of residual enthalpies and residual entropies by Eqs. ( (5.54)and ( 5.55)is straightforward for given valnes of T, P, and composition, provided one has sufticient data to evaluate B and dB/dT. The range of applicability of these equations is the same as for Eq. (3.37), as discnssed in Sec. 3.4. 

Equations (6.46) tluough (6.48) are incompatible with pressnre-explicit equations of state, and mnstbetransfonnedto make V (ordensity p)thevariableofintegration.ln application p is a more convenient variable than V, and the equation, PV = ZRT, is written in the 

Differentiation of Eq. (6.56) provides the first derivative on tlie right, and differentiation of Eq. ( 6.57 provides tile second. Snbstitutionfeads to  

The tliree-term viriaf equation, Eq. (3.39) is tlie simplest pressure-explicit equation of 

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