What is the magnitude of work performed by one mole of the gas when its volume increases 8 times if — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Given $C_v = 1.5R$, the gas is monoatomic ($\gamma = 5/3$). From previous, $x-1 = (\frac{5}{3}-1)/2 = 1/3$. The relation is $TV^{1/3} = \text{const}$. $T_2 = T_1(V_1/V_2)^{1/3} = 300(1/8)^{1/3} = 150\text{ K}$. $\Delta T = -150\text{ K}$. From first law, $\Delta U = q + W = -\Delta U + W \implies W = 2\Delta U$. $\Delta U = 1 \times 1.5R \times (-150) = -225R$. $W = 2(-225R) = -450R$. Using $R \approx 2\text{ cal/K-mol}$, magnitude of work is $450 \times 2 = 900\text{ cal}$.