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JEE Main & Advanced Physics Thermodynamical Processes Question Bank Self Evaluation Test - Thermodynamics

  • question_answer
    A Carnot engine operating between temperatures \[{{T}_{1}}\]and \[{{T}_{2}}\] has efficiency\[\frac{1}{6}\]. When \[{{T}_{2}}\] is lowered by 62 K its efficiency increases to \[\frac{1}{3}\]. Then \[{{T}_{1}}\]and \[{{T}_{2}}\] are, respectively

    A) 372 K and 330 K           

    B) 330 K and 268 K

    C) 310 K and 248 K

    D)        372 K and 310 K

    Correct Answer: D

    Solution :

    [d] \[{{\eta }_{1}}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\Rightarrow \frac{1}{6}=1-\frac{{{T}_{2}}}{{{T}_{1}}}\Rightarrow \frac{{{T}_{2}}}{{{T}_{1}}}=\frac{5}{6}\]        ...(i) \[{{\eta }_{2}}=1-\frac{{{T}_{2}}-62}{{{T}_{1}}}\Rightarrow \frac{1}{3}=1-\frac{{{T}_{2}}-62}{{{T}_{1}}}\]              ?(ii) On solving Eqs. (i) and (ii) \[{{T}_{1}}=372K\] and \[{{T}_{2}}=310K\]


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