Problem 2.197

Demonstrate that Eqs. $(2.6 \mathrm{a})$ and $(2.6 \mathrm{~b})$ are valid for a substance, obeying the Van der Waals equation, in critical state.

2.6(a) Relations between Van der Waals constants and the parameters of the critical state of a substance:

$$V_{M \mathrm{c} r}=3 b, p_{\mathrm{cr}}=\frac{a}{27 b^{2}}, \quad T_{\mathrm{cr}}=\frac{8 a}{27 R b}$$

2.6(b) Relation between the critical parameters for a mole of substance:

$$p_{\mathrm{cr}} V_{M \mathrm{cr}}=(3 / 8) R T_{\mathrm{c} r}$$

Instruction. Make use of the fact that the critical state corresponds to the point of inflection in the isothermal curve $p(V)$.