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:

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