One mole of oxygen undergoes a cyclic process in which volume of the gas change $$10$$ times within the cycle, as shown in the figure. Process: AB and CD are adiabatic. Find the efficiency of the process, in percent. Take $$(10)0.4$$ $$=2.5$$.

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Infinity Learn · Accepted Answer

$$n=1$$,γ$$=75$$⇒ γ−$$1=25$$ $$QAB=QCD=0Let$$ $$TA=T1$$ and $$TD=T2$$ with $$T2$$>$$T1For$$ the process AB, we have    TVγ−$$1=$$ constant ⇒$$TV25=$$ constant ⇒$$TA10V025=TBV025$$⇒$$TB=T1(10)0.4$$≈$$2.5T1Similarly$$, $$TC=2.5T2Now$$, $$QBC=CV$$ΔT⇒$$QBC=52RTC$$−$$TB=(6.25R)T2$$−$$T1$$ and      $$QDA=$$−$$2.5RT2$$−$$T1So$$, Wnet $$=Qnet$$ $$=3.75RT2$$−$$T1$$     $${$$∵Δ$$U=0}$$⇒ η$$=Wnet$$  heat absorbed ×$$100=3.756.25$$×$$100=60$$%

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