Two rigid adiabatic vessels A (volume = 4 L) and B (volume = 6 L), which initially contains two gase — Thermodynamics and Thermochemistry Chemistry Question
Question
Two rigid adiabatic vessels A (volume = 4 L) and B (volume = 6 L), which initially contains two gases at different temperatures, are connected by a pipe of negligible volume. The vessel A contains 2 moles of Ne gas ($C_{P,m} = 5 \text{ cal/K-mol}$) at 300 K and vessel B contains 3 moles of $\text{SO}_2$ gas ($C_{P,m} = 8 \text{ cal/K-mol}$) at 400 K. What is the final pressure (in atm) when the valve is opened and 12 kcal heat is supplied through it to the vessels?
💡 Solution & Explanation
Initial $U = 2(3)(300) + 3(6)(400) = 1800 + 7200 = 9000\text{ cal}$. Heat added = 12000 cal. Final $U = 21000\text{ cal}$. Final temperature $T_f$ dictates $24 T_f = 21000 \implies T_f = 875\text{ K}$. Final pressure $P = \frac{(5)(0.0821)(875)}{10} \approx 35.9\text{ atm}$, closely mapped to 35 atm option.