Question

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.

• A. \( C_B = \infty, \, C_A = 0 \)
• B. \( C_A = 0 \, \text{and} \, C_B = \infty \)
• C. \( C_P > C_V > C_A = C_B \)
• D. \( C_A > C_P > C_V \)

Answer 1

The Correct Option is B

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:

\[ C_A = 0 \quad \text{and} \quad C_B = \infty \]