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Question 40

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

For an adiabatic process, $$Q = 0$$ (no heat exchange with the surroundings).

From the first law of thermodynamics:

$$\Delta U = Q - W = -W$$

$$W = -\Delta U$$

For an ideal gas, the internal energy depends only on temperature:

$$\Delta U = nC_v\Delta T$$

Therefore:

$$W = -nC_v\Delta T$$

This shows that the work done in an adiabatic process depends only on the change in temperature (for a given amount of ideal gas with fixed $$C_v$$).

The answer is Option A: change in its temperature.

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