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JEE Main & Advanced Physics Thermodynamical Processes Question Bank Critical Thinking

  • question_answer
    Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at \[{{T}_{1}}=800k\] and rejects to sink at \[{{T}_{2}}k.\]. The second engine B receives heat rejected by the first engine and rejects to another sink at \[{{T}_{3}}=300k.\] If the work outputs of two engines are equal, then the value of \[{{T}_{2}}\] is

    A)            100K                                        

    B)            300K

    C)            550K                                        

    D)            700K

    Correct Answer: C

    Solution :

                       \[{{\eta }_{A}}=\frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{1}}}=\frac{{{W}_{A}}}{{{Q}_{1}}}\]Þ\[{{\eta }_{B}}=\frac{{{T}_{2}}-{{T}_{3}}}{{{T}_{2}}}=\frac{{{W}_{B}}}{{{Q}_{2}}}\]                    \ \[\frac{{{Q}_{1}}}{{{Q}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}}\times \frac{{{T}_{2}}-{{T}_{3}}}{{{T}_{1}}-{{T}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}}\] \ \[{{W}_{A}}={{W}_{B}}\]            \ \[{{T}_{2}}=\frac{{{T}_{1}}+{{T}_{3}}}{2}=\frac{800+300}{2}=550K\]


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