JEE Physics 2025 Question with Solution

Given: An adiabatic process.

Find: Which statement is true.

In an adiabatic process, there is no heat exchange, so

$$dQ = 0$$

The molar heat capacity is

$$C = \frac{1}{n}\frac{dQ}{dT}$$

Therefore,

$$C = \frac{1}{n}\frac{0}{dT} = 0$$

Using the first law of thermodynamics,

$$\Delta Q = \Delta U + W$$

For an adiabatic process,

$$0 = \Delta U + W$$

So,

$$W = -\Delta U$$

Hence, work done by the gas is equal to the decrease in internal energy, not the increase.

Also, for an ideal gas,

$$\Delta U = nC_v\Delta T$$

so internal energy increases when temperature increases.

Therefore, the correct option is C.

Given: The process is adiabatic.

Find: Which option is correct.

For an adiabatic process,

$$dQ = 0$$

1. Option A: "The molar heat capacity is infinite"

Molar heat capacity is defined as

$$C = \frac{1}{n}\frac{dQ}{dT}$$

Since $dQ = 0$,

$$C = 0$$

So this statement is false.

2. Option B: "Work done by the gas equals the increase in internal energy"

From the first law,

$$\Delta Q = \Delta U + W$$

With $\Delta Q = 0$,

$$0 = \Delta U + W$$ $$W = -\Delta U$$

Thus, work done by the gas equals the decrease in internal energy. So this statement is false.

3. Option C: "The molar heat capacity is zero"

Since $dQ = 0$,

$$C = \frac{1}{n}\frac{dQ}{dT} = 0$$

This statement is correct.

4. Option D: "The internal energy of the gas decreases as the temperature increases"

For an ideal gas,

$$\Delta U = nC_v\Delta T$$

Since $C_v > 0$, internal energy increases with temperature. So this statement is false.

Therefore, the only true statement is The molar heat capacity is zero, so the correct option is C.