JEE Physics 2025 Question with Solution

Given: The pressure of an ideal gas increases linearly with temperature.

Find: Which statements among A, B, C, D, E are correct.

For an ideal gas,

If $P$ increases linearly with $T$, then $\frac{P}{T} = \frac{nR}{V}$ remains constant, so $V$ remains constant. Therefore, the process is isochoric.

Now examine each statement:

1. A. In an isochoric process, $\Delta V = 0$, so work done by the gas is

Hence, A is true.

2. B. From the first law of thermodynamics,

Since $W = 0$ for an isochoric process,

So the heat added is not different from the change in internal energy. Hence, B is false.

3. C. Since volume remains constant, the volume does not increase. Hence, C is false.

4. D. For an ideal gas, internal energy depends only on temperature. As temperature increases, internal energy increases. Hence, D is true.

5. E. Because $P \propto T$ for constant $V$, the process is isochoric. Hence, E is true.

Therefore, the correct statements are A, D, E only. The correct option is B.

Given: Pressure increases linearly with temperature for an ideal gas.

Find: The correct combination of statements.

Using the ideal gas equation,

This is a linear relation between $P$ and $T$ when $n$ and $V$ are constant. Hence the process is at constant volume.

Because the process is isochoric:

so,

Also, from the first law,

Thus heat supplied equals the change in internal energy, not different from it.

Further, for an ideal gas,

So when temperature increases, internal energy increases. Since volume is constant, there is no increase in volume.

Hence:

• A true
• B false
• C false
• D true
• E true

Therefore, the correct option is B.