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JEE Main & Advanced Physics Thermodynamical Processes JEE PYQ-Thermodynamical Processes

  • question_answer
    Two Carnot engines A and B are operated in series. The first one, A, receives heat at \[{{T}_{1}}\left( =600\text{ }K \right)\] and rejects to a reservoir at temperature Ta. The second engine B receives heat rejected by the first engine and, in turn, rejects to a heat reservoir at\[{{T}_{3}}(=400\text{ }K)\]. Calculate the temperature \[{{T}_{2}}\] if the work outputs of the engines are equal: [JEE Main 09-Jan-2019 Evening]

    A)  500 K          

    B)  300 K

    C)  600 K              

    D)       400 K

    Correct Answer: A

    Solution :

    [a] \[W={{Q}_{1}}-{{Q}_{2}}\]
    \[W={{Q}_{2}}-{{Q}_{3}}\]
    \[{{Q}_{1}}-{{Q}_{2}}={{Q}_{2}}-{{Q}_{3}}\]
    \[{{T}_{1}}-T=T-{{T}_{3}}\]
    \[2T={{T}_{1}}-{{T}_{3}}\]
    \[T=\frac{{{T}_{1}}+{{T}_{3}}}{2}=500\,\,K\]


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