The compressibility factor (Z) of a gas at cr | vedclass

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(C) Given, $T_c = \frac{8 a}{27 R b}$, $p_c = \frac{a}{27 b^2}$, $V_c = 3 b$. The compressibility factor $(Z)$ is defined as $Z = \frac{p V}{R T}$. At

Vedclass · Accepted Answer

$3/8$

Vedclass · Answer

(C) Given, $T_c = \frac{8 a}{27 R b}$, $p_c = \frac{a}{27 b^2}$, $V_c = 3 b$. The compressibility factor $(Z)$ is defined as $Z = \frac{p V}{R T}$. At the critical state, $Z = \frac{p_c V_c}{R T_c}$. Substituting the given values: $Z = \frac{(\frac{a}{27 b^2}) 	imes (3 b)}{R 	imes (\frac{8 a}{27 R b})}$. $Z = \frac{\frac{3 a}{27 b}}{\frac{8 a}{27 b}} = \frac{3}{8}$. Thus, the correct option is $(C)$.

The compressibility factor $(Z)$ of a gas at critical state is $(T_c = \frac{8 a}{27 R b}; p_c = \frac{a}{27 b^2}; V_c = 3 b)$.

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