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Figure. Shows an ideal gas changing its state `A` to state `C` by two different path `ABC` and `AC`. a. Find the path along which the work done is the least. b. The internal energy of the gas at `A` is `10 J` and the amount of heat supplied to change its state to `C` through the path `AC` is `200 J`. Find the internal energy at `C`. c. The internal energy of the gas at state `B` is `20 J`. Find the amount of heat supplied to the gas to go from state `A` to state `B`. |
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Answer» (i) for path ABC, `W= W_(AB)+W_(BC)=P(V_(B)-V_(A))+P_(B)(V_(C)-V_(B))` `= zero + 15 (6-2)= 60J` For path AC, `W_(AC)= "area" ACFEA= "area of" DeltaACD+ area of rectangular ADFE` `=1/2ADxxDC+ADxxFD= 1/2xx4xx10+4xx5= 40J` `:.` work done is least along the path AC. (ii) `U_(A)= 10J, DeltaQ_(AC)=200J` According to first law of thermodynamics, `DeltaQ_(AC)=DeltaU_(AC)+DeltaW_(AC)=(U_(C)-U_(A))+ DeltaW_(AC)` `U_(C)= DeltaQ_(AC)+U_(A)-DeltaW_(AC)= 200+10-40= 170J` (iii) `U_(B)= 20J, DeltaQ_(AB)=?` According to first law of thermodynamics , `DelatQ_(AB)= DeltaU_(AB)+DeltaW_(AB)=(U_(AB)-U_(A))+DeltaW_(AB)` `DelatQ_(AB)= (20-10)+Zero= 10J` |
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