JEE Physics 2024 Question with Solution

Given: Two thermodynamical processes $A$ and $B$ are identified from a $\log P$ vs. $\log V$ figure. Find: the correct relation among $C_A$, $C_B$, $C_P$ and $C_V$.

From the solution, process $A$ has slope $\tan^{-1}\gamma$ where

so process $A$ is adiabatic, using

For an adiabatic process,

Hence the molar heat capacity for process $A$ is

Process $B$ has slope $45^\circ$ or $\tan^{-1}1$, so it is isothermal, using

For an isothermal process, temperature does not change. Thus heat supplied is used in work done, and the effective molar heat capacity tends to

Therefore, the correct statement is $C_A = 0$ and $C_B = \infty$. The correct option is B.

Given: The graph distinguishes two processes $A$ and $B$ in a $\log P$ vs. $\log V$ plot. Find: which option matches their molar heat capacities.

The extracted solution states that process $A$ corresponds to an adiabatic path and process $B$ corresponds to an isothermal path.

For the adiabatic path,

By definition, the process heat capacity is zero, so

For the isothermal path, the temperature remains constant. A finite amount of heat can be exchanged while

Therefore, from the process heat capacity idea, the ratio $\frac{dQ}{dT}$ becomes unbounded, giving

Hence the final answer remains $C_A = 0$ and $C_B = \infty$, so the correct option is B.