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 (a) Compressing the gas isothermally or adiabatically will require the same amount of work. (b) Which of the case (whether compression through isothermal or through adiabatic process) requires more work will depend upon the atomicity of the gas. (c) Compressing the gas isothermally will require more work to be done. (d) Compressing the gas through adiabatic process will require more work to be done.

Answer: (d). Work done on the gas = area under the P – V curve from V to V/2. In adiabatic compression the temperature rises, so pressure rises faster ( PVγ = const, γ > 1) than in isothermal ( PV = const). The adiabatic curve lies above the isothermal one over the same volume change, so its area is larger. So the answer is (d) adiabatic compression needs more work.

A gas is compressed isothermally to half its initial volume. The same… | NEET 2016 (Phase 1)

Q223NEET 2016 · PHASE 1Medium

Thermodynamic Processes

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

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Answer: (d)

Work done on the gas = area under the $P$ – $V$ curve from $V$ to $V/2$ .
In adiabatic compression the temperature rises, so pressure rises faster ( $PV^{\gamma}$ = const, $\gamma > 1$ ) than in isothermal ( $PV$ = const).
The adiabatic curve lies above the isothermal one over the same volume change, so its area is larger.
So the answer is (d) adiabatic compression needs more work.

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