Figure shows a cyclic process performed on one mole of an ideal gas. A total of $$1000$$ J of heat is withdrawn from the gas in a complete cycle. Find the work done $$on/by$$ the gas, in joule, during the process B→C. Given R $$=$$ $$8.3$$ J $$mol-1$$ $$K-1$$

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Infinity Learn · Accepted Answer

For a cyclic process, Δ$$U=0$$⇒ Qcycle $$=Wcycle$$    ……..(1)where$$, Wcycle $$=WA$$→$$B+WB$$→$$C+WC$$→A …….$$(2)Process$$ C→A is isochoric, hence WC→$$A=0Process$$ A →B is isobaric, as its $$T-V$$ graph is a straight line passing through origin.In an isobaric process, work done is         WA→$$B=PVB$$−$$VA=nRTB$$−TA⇒ WA→$$B=1$$×$$8.3(400$$−$$300)=830J$$    ........$$(3)WA$$→B is positive, so expansion of gas takes place.From equations $$(1), (2) and (3), we get−$$1000=830+WB$$→$$C+0$$⇒ WB→$$C=$$−$$1830$$ JNegative work done implies that compression of the gas takes place or work is done on the $$system/gas$$.

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