Two moles of an ideal gas () was compressed adiabatically against constant pressure of 2 atm, which — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

For adiabatic compression, $W = \Delta U = n C_v (T_2 - T_1)$. First, find $T_2$ using $-P_{ext}(\frac{nR T_2}{P_2} - \frac{nR T_1}{P_1}) = n C_v (T_2 - T_1)$. $-2 \times (\frac{T_2}{2} - \frac{350}{1}) = \frac{5}{2} (T_2 - 350) \implies -(T_2 - 700) = 2.5 T_2 - 875 \implies 3.5 T_2 = 1575 \implies T_2 = 450 \text{ K}$. Work done $= \Delta U = 2 \times \frac{5}{2} R \times (450 - 350) = 5R \times 100 = 500 R$.