One mole of a real gas is subjected to heating at constant volume from () state to () state. Then it — Thermodynamics and Thermochemistry Chemistry Question
Question
One mole of a real gas is subjected to heating at constant volume from ($P_1, V_1, T_1$) state to ($P_2, V_1, T_2$) state. Then it is subjected to irreversible adiabatic compression against constant external pressure of $P_3$ atm, till the system reaches final state ($P_3, V_2, T_3$). If the constant volume molar heat capacity of real gas is $C_V$, then the correct expression for $\Delta H$ from State 1 to State 3 is
Answer: C
💡 Solution & Explanation
$\Delta U_{\text{total}} = \Delta U_1 + \Delta U_2 = C_V(T_2 - T_1) + [-P_3(V_2 - V_1)]$. Enthalpy is $\Delta H = \Delta U_{\text{total}} + P_3 V_2 - P_1 V_1$. Substituting $\Delta U$ yields $\Delta H = C_V(T_2 - T_1) - P_3 V_2 + P_3 V_1 + P_3 V_2 - P_1 V_1 = C_V(T_2 - T_1) + P_3 V_1 - P_1 V_1$.
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