Two moles of an ideal gas () is subjected to the following changes in states:<br><br><br><br>The cor — Thermodynamics and Thermochemistry Chemistry Question
Question
Two moles of an ideal gas ($C_{v,m} = 1.5 R$) is subjected to the following changes in states:<br>$\text{A (500 K, 5 bar)} \xrightarrow{\text{Reversible Isothermal Expansion}} \text{B}$<br>$\text{B} \xrightarrow{\text{Isochoric Cooling}} \text{C (250 K, 1 bar)}$<br>$\text{C} \xrightarrow{\text{Single stage adiabatic compression}} \text{D (3 bar)}$<br>The correct statement(s) is/are
Answer: A,B,C
💡 Solution & Explanation
Path B to C is isochoric, so $P_B/T_B = P_C/T_C \implies P_B/500 = 1/250 \implies P_B = 2.0\text{ bar}$. C to D is single stage adiabatic compression against 3 bar: $-3(V_D - V_C) = n C_v (T_D - T_C)$. Solving this dynamically yields $T_D = 450\text{ K}$. $\Delta H_{\text{CD}} = n C_p \Delta T = 2(2.5R)(200) = 1000 R$.
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