A gas is taken from $$state-1$$ to $$state-2$$ along the path shown in figure. If $$70$$ cal of heat is extracted from the gas in the process, calculate the change in internal energy of the system (in$$ $$J).

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Infinity Learn · Accepted Answer

We know work done by a gas is given by the area under $$PV-curve$$ or the area between $$PV-curve$$ and the volume axis. Generally, we take volume on $$x-axis$$ while plotting  $$V-curve$$ but in figure it is taken on $$y-axis$$ thus the work done is given by the shaded area shown in figure. In this process volume of gas decreases thus work is done on the gas and it is given $$asW=$$−$$12$$×$$1.5$$×$$10$$−$$4$$×(2+5)×$$105=$$−$$52.5JIt$$ is given that heat extracted in the process is $$70$$ cal, thus    $$Q=$$−$$70$$ $$cal=70$$×$$4.2$$ $$J=$$−$$294$$ JNow from first law of thermodynamics, we $$haveQ=W+$$ΔUor Δ$$U=Q$$−$$W=($$−$$294)$$−$$($$−$$52.5)=$$−$$241.5JThus$$ in the process internal energy of gas decreases by $$241.5$$ J

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