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JEE Main & Advanced Physics Kinetic Theory of Gases Question Bank Self Evaluation Test - Kinetic Theory

  • question_answer
    Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is \[22{}^\circ C.\] During the day, temperature rises to \[42{}^\circ C\] and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately      

    A) 212 kPa

    B) 209 kPa

    C) 206 kPa

    D) 200 kPa

    Correct Answer: B

    Solution :

    [b] \[\frac{{{P}_{1}}{{V}_{1}}}{{{T}_{1}}}=\frac{{{P}_{2}}{{V}_{2}}}{{{T}_{2}}}\]                      Here, \[{{P}_{1}}=200kPa\] \[{{T}_{1}}=22{}^\circ C=295K~~~~~~{{T}_{2}}=42{}^\circ C=315K\] \[{{V}_{2}}={{V}_{1}}+\frac{2}{100}{{V}_{1}}=1.02{{V}_{1}}\] \[\therefore \,\,\,\,\,{{P}_{2}}=\frac{200\times 315{{V}_{1}}}{295\times 1.02{{V}_{1}}}=209.97kPa\]


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