Question

Assertion (A): When an ideal gas is compressed adiabatically its temperature and the average kinetic energy of gas molecules increase.
Reason (R): The kinetic energy increases because of collisions of molecules with moving parts of the container walls only.

• (A) and (R) are true and (R) is correct explanation of (A)
• (A) and (R) are true but (R) is not correct explanation of (A)
• (A) is true and (R) is false
• (A) is false and (R) is true

Hint:

In adiabatic compression, no heat enters the gas. The increase in temperature occurs because external work done on the gas increases its internal energy.

Answer 1

The Correct Option is A

Step 1: Analyze Assertion (A).
In an adiabatic compression, \[ Q=0 \] That means no heat is exchanged with surroundings.
When the gas is compressed, work is done on the gas.
According to the first law of thermodynamics, \[ \Delta U=Q+W \] Since \[ Q=0, \] we get \[ \Delta U=W \] Thus, internal energy of the gas increases.
For an ideal gas, internal energy depends only on temperature.
Therefore, temperature increases.
Also, average kinetic energy of gas molecules is directly proportional to absolute temperature: \[ \text{Average KE}\propto T \] Hence, average kinetic energy also increases.
Therefore, Assertion (A) is true.

Step 2: Analyze Reason (R).
During compression, the walls (or piston) move inward.
Gas molecules collide with the moving wall and rebound with greater speed.
Thus, molecules gain kinetic energy due to collisions with the moving walls.
Hence, Reason (R) is true.

Step 3: Check whether Reason correctly explains Assertion.
The increase in molecular kinetic energy during adiabatic compression occurs because moving walls transfer energy to the gas molecules during collisions.
This raises the internal energy and temperature of the gas.
Therefore, Reason (R) correctly explains Assertion (A).

Step 4: Final conclusion.
Hence, \[ \boxed{\text{(A) and (R) are true and (R) is the correct explanation of (A)}} \]