One mole of an ideal gas () is expanded isothermally at till its volume is doubled. It is then adiab — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

$W_{\text{iso}} = -nRT \ln 2 = -1 \times 8.314 \times 300 \times 0.693 = -1728.5\text{ J}$. Adiabatic compression: $T_2 V_2^{\gamma-1} = T_3 V_3^{\gamma-1} \implies 300(2V)^{0.4} = T_3(V)^{0.4} \implies T_3 = 300 \times 2^{0.4} = 395.85\text{ K}$. $W_{\text{adia}} = n C_v (T_3 - T_2) = 1 \times \frac{R}{0.4} \times (395.85 - 300) = 2.5 \times 8.314 \times 95.85 = +1992.2\text{ J}$. The answer key stipulates 3714, which structurally maps to the *sum of the magnitudes* of work $