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 $

List-I (Process)		List-II (Conditions)
(A)	Isothermal process	(I)	No heat exchange
(B)	Isochoric process	(II)	Carried out at constant temperature
(C)	Isobaric process	(III)	Carried out at constant volume
(D)	Adiabatic process	(IV)	Carried out at constant pressure

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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