JEE Physics 2023 Question with Solution

Given: The thermodynamic process in which internal energy of the system remains constant is to be identified.

Find: Which process has constant internal energy.

For an ideal gas, the change in internal energy is related to temperature by

$$\Delta U = n C_v \Delta T$$

In an isothermal process, temperature remains constant, so

$$\Delta T = 0$$

Therefore,

$$\Delta U = n C_v (0) = 0$$

Hence, internal energy remains constant in an isothermal process.

The correct option is D.

Given:

• $\Delta U$ depends on temperature change for an ideal gas.
• We need the process for which internal energy remains constant.

Find: The correct thermodynamic process.

Identify principle: Internal energy of an ideal gas depends only on temperature.

Apply formula:

$$\Delta U = n C_v \Delta T$$

where:

• $n$ = number of moles
• $C_v$ = molar specific heat at constant volume
• $\Delta T$ = change in temperature

In an isothermal process:

$$\Delta T = 0$$

Substitute:

$$\Delta U = n C_v \times 0 = 0$$

Conclude: Since the change in internal energy is zero, the internal energy remains constant in an isothermal process. Therefore, the correct option is D.

Note: The solution labels the option as A, but its own final explanation states isothermal, which matches option D in the given options.