An amount of heat is added to a monoatomic ideal gas in a process in which the gas performs a work o — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

Heat $q = Q$. Work done by gas is $Q/2 \implies W = -Q/2$. Internal energy change $\Delta U = q + W = Q - Q/2 = Q/2$. For a monoatomic gas, $\Delta U = nC_V\Delta T \implies n(1.5R)\Delta T = Q/2 \implies n\Delta T = Q/3R$. Molar heat capacity $C = q / (n\Delta T) = Q / (Q/3R) = 3R$. Using $R \approx 2\text{ cal/K-mol}$, $C = 3 \times 2 = 6\text{ cal/K-mol}$.