The procedure for calculation of the residual enthalpy for a pure gas is shown in Example 8.5. Now consider the residual enthalpy for a binary gas mixture. For this calculation, it is necessary to determine da/dT for the mixture.

(a) Write the form of this derivative for a binary mixture in terms of da₁/dT and da₂/dT based on the conventional quadratic mixing rule and geometric mean combining rule with a nonzero k_ij.

(b) Provide the expression for the residual enthalpy for a binary mixture that follows the Peng-Robinson equation.

(c) A mixture of 50 mol% CO₂ and 50 mol% N₂ enters a valve at 7 MPa and 40°C. It exits the valve at 0.1013 MPa. Explain how you would determine whether CO₂ precipitates, and if so, whether it would be a liquid or solid.

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Example 8.5 Enthalpy departure for the Peng-Robinson equation Obtain a general expression for the enthalpy departure function of the Peng-Robinson equation.