A system undergoes three $$quasi-static$$ processes sequentially as indicated in the given figure. $$1-2$$ is an isobaric process, $$2-3$$ is a polytropic process with γ $$=$$ $$4/3$$ and $$3-1$$ is a process in which $$PV=$$ constant. $$P2$$ $$=$$ $$P1$$ $$=$$ $$4$$ x $$105$$ $$N/m2$$, $$P3$$ $$=1$$ x $$105$$ $$N/m2$$ and $$V1$$ $$=$$ $$1$$ $$m3$$.The heat transfer for the cycle is ΔQ, the change in internal energy is ΔU and the work done is ΔW. Then

Question

A system undergoes three $$quasi-static$$ processes sequentially as indicated in the given figure. $$1-2$$ is an isobaric process, $$2-3$$ is a polytropic process with γ $$=$$ $$4/3$$ and $$3-1$$ is a process in which $$PV=$$ constant. $$P2$$ $$=$$ $$P1$$ $$=$$ $$4$$ x $$105$$ $$N/m2$$, $$P3$$ $$=1$$ x $$105$$ $$N/m2$$ and $$V1$$ $$=$$ $$1$$ $$m3$$.The heat transfer for the cycle is ΔQ, the change in internal energy is ΔU and the work done is ΔW. Then

Infinity Learn · Accepted Answer

For the process $$3$$→$$1P1V1=P3V3$$⇒$$V3=P1V1P3=4$$×$$105$$×$$11$$×$$105=4m3For$$ the process $$2$$→$$3P2V2$$γ$$=P3V3$$γ⇒$$V2=P3P21$$γ$$V3=41434=414m3=2m3For$$ the process $$1$$→$$2$$,$$W12=P1V2$$−$$V1=(2$$−$$1)4$$×$$105JFor$$ the process $$2$$→$$3$$,$$W23=P2V2$$−$$P3V3($$γ−$$1)=(42$$−$$1$$×$$4)$$×$$10543$$−$$1=12(2$$−$$1)$$×$$105JFor$$ the process $$3$$→$$1$$,$$W31=$$−$$P1V1ln$$⁡$$V3V1$$ $$=$$−$$4$$×$$105$$×$$1$$×ln⁡$$41$$Δ$$U=0$$ Δ$$Q=$$Δ$$U+$$Δ$$W1$$→$$2$$→$$3$$→$$1=4$$×$$105(2$$−$$1)+12$$×$$105(2$$−$$1)$$−$$4$$×$$105$$×$$1.386$$≃$$1.08$$×$$105J$$Δ$$Q=$$ΔW≃$$1.08$$×$$105J$$

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