Thermodynamics — Medium JEE physics MCQ
An ideal gas expands isothermally from volume $V$ to $2V$. If the same gas expands from volume $V$ to $2V$ adiabatically, then the work done in isothermal expansion is:
- A. Greater than adiabatic work
- B. Less than adiabatic work
- C. Equal to adiabatic work
- D. Cannot be determined
Solution
For expansion from $V$ to $2V$:
In a P-V diagram, the isothermal curve lies above the adiabatic curve (since isothermal has $PV = $ constant, while adiabatic has $PV^\gamma = $ constant with $\gamma > 1$).
Work done = Area under the P-V curve
Since the isothermal curve is above the adiabatic curve during expansion, the area under the isothermal curve is greater.
Therefore, **isothermal work > adiabatic work**.
Alternatively: In isothermal expansion, heat is absorbed to maintain temperature, so more work can be extracted. In adiabatic expansion, the gas cools down, reducing pressure faster, leading to less work.