Question 114 of 190

Starting with the same initial conditions, an ideal gas expands from volume ${V}_{1}$ to ${V}_{2}$ in three different ways. The work done by the gas is ${W}_{1}$ if the process is purely isothermal, ${W}_{2}$, if the process is purely adiabatic and ${W}_{3}$ if the process is purely isobaric. Then, choose the correct option

A${W}_{2}\lt {W}_{1}\lt {W}_{3}$B${W}_{1}\lt {W}_{2}\lt {W}_{3}$C${W}_{2}\lt {W}_{3}\lt {W}_{1}$D${W}_{3}\lt {W}_{1}\lt {W}_{2}$

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Answer: (A) ${W}_{2}\lt {W}_{1}\lt {W}_{3}$

As we know, in isobaric process pressure remains constant and magnitude of slope of adiabatic curve will be more than the isothermal curve at the common point, therefore diagram for process will be as given below.

Also, $W=$ area under $P-V$ curve.
Hence,
$∴{W}_{2}\lt {W}_{1}\lt {W}_{3}$