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# (a) 17 m³ mol-1 of gaseous toluene at 19°C is compressed from 1 bar to 2.5 bar ina pressure vessel. In order to keep the temperature of the fluid constant,

heat needs to be removed from the system. Calculate the heat transferred during this process, assuming that toluene behaves as a Redlich-Kwong fluid. Given T. =592 K, Pc = 41.3 bar, w =0.266, C, = 1.72 kJ (kg K)-1 and[9 marks] \left(\frac{\partial V}{\partial T}\right)_{P}=-\frac{\left(\frac{\partial P}{\partial T}\right)_{V}}{\left(\frac{\partial P}{\partial V}\right)_{T}} (b) For the Berthelot EOS, P(v-b)=A T-\frac{a(v-b)}{T v^{2}}, \text { with } a=\frac{27}{64} \frac{R^{2} T_{c}^{3}}{P_{c}} \text { and } b=\frac{1}{8} \frac{A T_{c}}{P_{c}} where v is the specific volume. Develop an expression for changes in specific entropy based on measurable properties (i.e., T, v and/or P) at isothermal conditions.[3 marks] (c) The excess Gibbs energy of a binary liquid mixture at constant temperature (T)and pressure (P) is given by: \frac{G^{E}}{R T}=\left(-2.6 x_{1}-1.8 x_{2}\right) x_{1} x_{2} Find expressions for In y1 and In 12 at T and P.

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