JEE Main & Advanced Sample Paper JEE Main - Mock Test - 30

  • question_answer
    A gas undergoes a cyclic process \[a-b-c-a\]which is as shown in the PV diagram. The process \[a-b\]is isothermal, \[b-c\]is adiabatic and \[c-a\]is a straight line on \[P-V\]diagram. Work done in process ab and be is \[5\text{ }J\]and \[4\text{ }J\]respectively. Calculate the efficiency of the cycle, if the area enclosed by the diagram abca in the figure is \[\text{3 }J\]

    A) \[0.15\]            

    B)                    \[0.4\]                    

    C)   \[0.25\]                  

    D)        \[0.6\]

    Correct Answer: D

    Solution :

    [d] \[{{W}_{AB}}=5J\] \[\Delta {{U}_{ab}}=0\] (isothermal) \[{{Q}_{ab}}=5J\] (First law) \[{{W}_{bc}}=4J\] \[{{Q}_{bc}}=0\] (Adiabatic) \[\Delta {{U}_{bc}}=-4J\] (Adiabatic) \[\Delta {{U}_{bc}}=-4J\] (First law) \[\therefore \,\,\,\,\,\Delta {{U}_{ab}}+\Delta {{U}_{bc}}+\Delta {{U}_{ca}}=0\] \[\therefore \,\,\,\,\,\,\Delta {{U}_{ca}}=4J\] Also, \[{{W}_{ab}}+{{W}_{bc}}+{{W}_{ca}}=3J\] (Area inside cycle) \[5+4+{{W}_{ca}}=3\] First law for process ca \[{{Q}_{ca}}=4-6=-2J\] Efficiency of cycle \[\eta =\frac{{{W}_{cycle}}}{{{Q}_{ab}}}=\frac{3}{5}=0.6\]


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