Two thermodynamical processes are shown in the figure. The molar heat capacity for process $ A $ and $ B $ are $ C_A $ and $ C_B $. The molar heat capacity at constant pressure and constant volume are represented by $ C_P $ and $ C_V $, respectively. Choose the correct statement.

Question

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Step 1. Understanding the Slopes in the log P vs. log V Diagram: Process A has a slope of $ \tan^{-1} \gamma $, where $ \gamma = \frac{C_P}{C_V} $, indicating an adiabatic process (since $ PV^\gamma = \text{constant} $). Process B has a slope of $ 45^\circ $ or $ \tan^{-1} 1 $, suggesting that it is an isothermal process (since $ PV = \text{constant} $). Step 2. Using Heat Capacities for Adiabatic and Isothermal Processes: For an adiabatic process ($ PV^\gamma = \text{constant} $), the heat capacity $ C_A $ is effectively zero because no heat exchange occurs ($ dQ = 0 $ for adiabatic). For an isothermal process ($ PV = \text{constant} $), the heat capacity $ C_B $ tends to infinity because any heat added is used to perform work without changing temperature. Conclusion: Therefore, the correct statement is: $$ C_A = 0 \quad \text{and} \quad C_B = \infty $$

Answer

$ C_B = \infty, \, C_A = 0 $

Answer

$ C_A = 0 \, \text{and} \, C_B = \infty $

Answer

$ C_P > C_V > C_A = C_B $

Answer

$ C_A > C_P > C_V $

Two thermodynamical processes are shown in the figure. The molar heat capacity for process \( A \) and \( B \) are \( C_A \) and \( C_B \). The molar heat capacity at constant pressure and constant volume are represented by \( C_P \) and \( C_V \), respectively. Choose the correct statement.

The Correct Option is B

Solution and Explanation

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