InterviewSolution
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InterviewSolution
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A monatomic gas undergoes a cycle consisting of two isothermals and two isobarics. The minimum and maximum temperatures of gas during the cycle are `T_(1)= 400 K` and `T_(2)=800 K`, respectively, and the ratio of maximum to minimum volume is 4. The volume at `B` isA. `1.5 V_(0)`B. `2 V_(0)`C. `3 V_(0)`D. `2.5 V_(0)` |
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Answer» Correct Answer - B Process `CB` is done at minimum temperature, while process `DA` is done at maximum temperature. Process `A rarr b(` isobaric `)` `(V_(A))/(V_(B))=(T_(A))/(T_(B))=(800)/(400)=2` hence` V_(B)=2V_(0)` `B rarr C(` isothermal `)` `C rarr D (` isobaric `)` `(V_(D))/(V_(C))=(T_(D))/(T_(C))implies V_(D)=2V_(0)` `D rarr(` isothermal `)` `W_(AB)=P(V_(B)-V_(A))=nRDT` `=nR(-400)=-400nR` `W_(BC)=nRT1n(V_(C))/(V_(B))=nR4001n(V_(0))/(2V_(0))` `=-400nR 1n2` `W_(CD)=P(V_(D)-V_(C))=nR(400)=400nR` `W_(DA)=nRT1n(V_(A))/(V_(D))` `=nRxx800 xx 1 n (2V_(0))/(V_(0))=800nR1n2` `Delta W=400nR1n2` `DeltaQ=` heat is extracted `Q_(CD)=nC_(p) DeltaT=n(5)/(4)R400=1000nR` `=800 n R 1 n 2= 1000 n R+800 nR 1 n 2` Efficiency `=(DeltaW)/( Delta Q)` `eta =(2 1n 2)/(5 +4 1n 2 ) xx 100%` |
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