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

  • question_answer
    The efficiency of an ideal gas with adiabatic exponent \['\gamma '\] for the shown cyclic process would be                        

    A) \[\frac{\left( 2\,l\text{n}2-1 \right)}{\gamma /\left( \gamma -1 \right)}\]

    B) \[\frac{\left( 1-2\,l\text{n}2 \right)}{\gamma /\left( \gamma -1 \right)}\]

    C) \[\frac{\left( 2l\text{n}2+1 \right)}{\gamma /\left( \gamma -1 \right)}\]

    D) \[\frac{\left( 2l\text{n}2-1 \right)}{\gamma /\left( \gamma +1 \right)}\]

    Correct Answer: A

    Solution :

    [a] \[{{W}_{AB}}=0,{{W}_{BC}}=P\Delta V=nR\Delta T=-nR{{T}_{0}}\] \[{{W}_{CA}}=nRT\ell n\frac{{{V}_{f}}}{{{V}_{i}}}=nR(2{{T}_{0}})\ell n2\] \[{{Q}_{BC}}=n{{C}_{p}}\Delta T=\left( \frac{nR\gamma }{\gamma -1} \right){{T}_{0}}\] \[\text{Efficieancy, }\eta =\frac{W}{Q}=\left[ \frac{2\ell n2-1}{\gamma /\left( \gamma -1 \right)} \right]\]


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