JEE Main & Advanced Physics Thermodynamical Processes Question Bank Topic Test - Thermodynamical Process (2021)

  • question_answer
    An ideal gas at \[{{27}^{o}}C\] is compressed adiabatically to \[\frac{8}{27}\] of its original volume.  If \[\gamma =\frac{5}{3}\],  then the rise in temperature is

    A) 450 K

    B) 375 K

    C) 225 K

    D) 405 K

    Correct Answer: B

    Solution :

    [b] \[\frac{{{T}_{2}}}{{{T}_{1}}}={{\left( \frac{{{V}_{1}}}{{{V}_{2}}} \right)}^{\gamma -1}}\Rightarrow {{T}_{2}}=300\,{{\left( \frac{27}{8} \right)}^{\frac{5}{3}-1}}=300\,{{\left( \frac{27}{8} \right)}^{\frac{2}{3}}}\]
    \[=300\,{{\left\{ {{\left( \frac{27}{8} \right)}^{1/3}} \right\}}^{2}}=800\,{{\left( \frac{3}{2} \right)}^{2}}=675K\]
    \[\Rightarrow \ \Delta T=675-300=375\ K\]

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