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Question

# An ideal gas has initial volume V and pressure P. If the volume of gas is doubled during expansion, then minimum work will be done in which thermodynamic process ?

A
Isobaric process
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B
Isothermal process
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C
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D
Same in all alone given process
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Solution

## The correct option is C Adiabatic process Wgas=∫P dV Hence, work done by gas in each process can be compared by estimating the area under their respective P−V graphs. Here, we have plotted the P−V curve for the given isobaric, isothermal, adiabatic processes for expansion of gas from V→2V. Since, slopeAdiabatic>slopeIsothermal Hence, curve of adiabatic process will be more steep compared to that of isothermal one. We get the following order for area under curve in magnitude: AIsobaric>AIsothermal>AAdiabatic ⇒WIsobaric>WIsothermal>WAdiabatic Hence, minimum work is done by gas in adiabatic process.

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