JEE Physics 2023 Question with Solution

Given: A gas is compressed adiabatically.

Find: Which statement is not true.

In an adiabatic process, there is no heat exchange between the system and its surroundings, i.e.

$$\Delta Q = 0$$

According to the first law of thermodynamics,

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

where $\Delta U$ is the change in internal energy and $W$ is the work done by the system.

Since there is no heat exchange in an adiabatic process,

$$0 = \Delta U + W$$

Hence,

$$\Delta U = -W$$

So, during adiabatic compression, the internal energy changes. Also, the work done on the gas increases its temperature, and no heat is supplied to the system.

Therefore, the statement "There is no change in the internal energy" is incorrect. The correct option is A.

The solution states option D, but the working clearly shows that the incorrect statement is option A.

Given: Adiabatic compression of a gas.

Find: Check each statement using the first law.

1. For an adiabatic process,

$$\Delta Q = 0$$

So statement D is true.

2. Using the first law,

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

With $\Delta Q = 0$,

$$\Delta U = -W$$

During compression, work is done on the gas, so the internal energy increases. Hence statement A is false.

3. In adiabatic compression, increase in internal energy raises the temperature, so statement B is true.

4. Statement C is consistent if interpreted as work done on the gas being equal to the increase in internal energy.

Therefore, the only statement that is not true is A.