The workdone in an adiabatic change in an ideal gas depends upon: — Solution | JEE Physics

MCQEasyJEE 2025Isothermal & Adiabatic Processes

The workdone in an adiabatic change in an ideal gas depends upon:

Answer

Correct answer:B

Standard Method

Given: An ideal gas undergoes an adiabatic change.

Find: On which quantity the work done depends.

In an adiabatic process, no heat is exchanged with the surroundings, and the process follows

PV^{\gamma} = \text{constant}

where $P$ is pressure, $V$ is volume, and $\gamma = \frac{C_p}{C_v}$ .

The work done in an adiabatic process is

W = \frac{P_1V_1 - P_2V_2}{\gamma - 1}

Using the adiabatic relation, this can also be written in a form involving volume change:

W = \frac{K\left(V_2^{1-\gamma} - V_1^{1-\gamma}\right)}{1-\gamma}

This shows that the work done depends on the change in volume during the adiabatic process.

Therefore, the correct option is B.

Assuming the work done depends only on pressure change is incorrect because pressure and volume are linked during an adiabatic process. The standard adiabatic work expression is obtained through the process relation involving volume, so focus on the volume change.
Choosing specific heat is incorrect because specific heat ratio $\gamma$ appears as a parameter in the formula, but the question asks what changes determine the work done in the process. The relevant changing quantity here is volume.
Confusing temperature change with the primary dependence can lead to the wrong option. Although work can be related to temperature difference, the adiabatic process relation used here shows the dependence through the change in volume.

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