Question

Assertion- Work done during free expansion of an ideal gas whether reversible or irreversible is positive.
Reason- During free expansion external pressure is always less than the pressure of the system.
(A) Both assertion and reason are true, reason is the correct explanation of assertion.
(B) Both assertion and reason are true, reason is the incorrect explanation of assertion.
(C) Assertion is correct but reason is incorrect.
(D) Both assertion and reason both are incorrect.

Answer 1

Hint: Work done on an ideal gas depends on the volume and pressure of the gas. Any factor affecting the volume and pressure will affect the work done too.

Complete step by step solution:
Let’s look at the answer to this question
*Work done by the gas is given by the formula:
*W = PdV
*Where, P is the external pressure and dV is the change in volume.
From the above relation we can see that the work done is directly dependent on the amount of external pressure.
*Now, in free expansion the gas expands freely which means that no external pressure is acting on the gas. So, we can say that the value of external pressure is 0 in case of free expansion.
*Therefore, the work done in this case will be 0 and the external pressure in this case will also be 0.
Hence, we conclude that the given assertion and reason both are incorrect.
So, option (D) is the correct answer.

Note: Free expansion of a gas takes place when a gas is expanded in vacuum. The expansion of gas takes place without countering any forces as the external pressure is zero. Although the volume changes but even then the work is 0 because of no external pressure.