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Question: Answered & Verified by Expert
A fixed mass of oxygen gas performs a cyclic process ABCA as shown in the figure. Efficiency of the cycle will be

           
PhysicsThermodynamicsJEE Main
Options:
  • A 3 ln 3 - 2 5 + 3 ln 3
  • B 3 ln 4 - 2 4 + 5 ln 3
  • C 3 ln 4 - 3 4 + 5 ln 3
  • D 3 ln 3 - 1 6 + 3 ln 4
Solution:
2682 Upvotes Verified Answer
The correct answer is: 3 ln 3 - 2 5 + 3 ln 3
A  →  B  isochoric as P is directly proportional to T

W AB = 0

Q AB = n C v 3 T  - T  

        = 5 2 nR 2 T  = 5 nRT  

B  C isothermal and thus Q = W as there won't be any change in internal energy.
W BC = nR 3 T  ln P B P C = 3 nRT  ln 3

        = 3 nRT  ln 3 = Q BC

C A isobaric process
W CA = P V A - V C = nR T A - 3 T  = - 2 n RT  

Efficiency of a cyclic process is given by

                   η = Work done in cyclic process Heat supplied to the system = W Q in

Efficiency η = 3 nRT A ln 3 - 2 nRT A 5 nRT A + 3 nRT A ln 3

                   = 3 ln 3 - 2 5 + 3 ln 3

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