Statistical Mechanics · Problem 9.3

Statistical Mechanics of Interacting Systems: The Method of Quantized Fields — R. K. Pathria

Physics — Statistical Mechanics · van-der-waals-gas-thermodynamics

Problem

(a) Show that for a gas obeying van der Waals' equation of state (9.3.9) CP−CV=Nk{1−2akTv3(v−b)2}−1C_P - C_V = Nk\left\{1 - \frac{2a}{kTv^3}(v-b)^2\right\}^{-1} (b) Also show that, for a van der Waals gas with constant specific heat CVC_V, an adiabatic process conforms to the equation (v−b)TCV/Nk=const;(v - b)T^{C_V/Nk} = \text{const}; cf. eqn. (1.4.30). (c) Further show that the temperature change resulting from an expansion of the gas (into vacuum) from volume V1V_1 to volume V2V_2 is given by T2−T1=N2aCV(1V2−1V1).T_2 - T_1 = \frac{N^2 a}{C_V}\left(\frac{1}{V_2} - \frac{1}{V_1}\right).

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