JEE Main 2024

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.

log P vs log V diagram

![log P vs log V diagram](https://www.edvaya.com/jee/physics/q30-logP-logV-2024.png) A). $C_B = \infty, C_A = 0$ B). $C_A = 0 	ext{ and } C_B = \infty$ C). $C_P > C_V > C_A = C_B$ D). $C_A > C_P > C_V$

Edvaya · Accepted Answer

The correct answer is $C_A = 0 	ext{ and } C_B = \infty$. **Solution:** The graph plots $\log P$ versus $\log V$. For any polytropic process $PV^n = K$, taking the logarithm yields $\log P = -n \log V + \log K$. Thus, the slope of a line on this graph is equal to $-n$. For Process A: The line has an angle whose tangent is $\gamma$ with the negative x-axis, making its slope $-\gamma$. This means $n = \gamma$, which corresponds to an adiabatic process. Therefore, the molar heat capacity $C_A = 0$. For Process B: The line has an angle of $45^\circ$ with the negative x-axis, making its slope $-1$. This means $n = 1$, which corresponds to an isothermal process ($PV = 	ext{constant}$). Therefore, the molar heat capacity $C_B = \infty$. The correct statement is $C_A = 0$ and $C_B = \infty$.

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Physics > Thermodynamics And Kinetic Theory > Thermodynamics

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