An ideal gas is compressed to half its initial volume by means of… | NEET 2015 (AIPMT)

Q226NEET 2015 · AIPMTMedium

Thermodynamic Processes

An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas?

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Answer: (c)

Work on the gas = area under the $P$ – $V$ curve for the same volume change $V \to V/2$ .
Isochoric: no volume change, $W = 0$ . Isobaric: $P$ stays at $P_0$ (least area of the rest).
Isothermal: $P$ rises to $2P_0$ ; adiabatic: $P$ rises to $2^{\gamma}P_0$ , the steepest curve with the largest area.
So the answer is (c) adiabatic.

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