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A gas is compressed isothermally to half its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:

1. Compressing the gas isothermally will require more work to be done.
2. Compressing the gas through adiabatic process will require more work to be done.
3. Compressing the gas isothermally or adiabatically will require the same amount of work.
4. Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas.

Correct answer: Compressing the gas through adiabatic process will require more work to be done.

Solution

In an isothermal process, the work done is given by W = nRT ln(Vf/Vi), while in an adiabatic process, the work done depends on the specific heat ratio (γ). For the same volume change, the adiabatic process requires more work because the temperature increases, leading to a higher pressure and thus more work against it.

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