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JEE Main 202127 JulyEvening Shift
Exam
JEE Main
Year
2021
Date
27 July
Shift
Evening Shift
Subject
Physics
Chapter
Thermodynamics

JEE Main 2021 · 27 July · Evening Shift · Physics · Thermodynamics

One mole of an ideal gas is taken through an adiabatic process...

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27°Cto37°C27 ° C to 37 ° C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R=8.314Jmol−1k−1]\left[R = 8 . 314J{mol}^{- 1}{k}^{- 1}\right]

Options

  1. Awork done by the gas is close to 332J332J
  2. Bwork done on the gas is close to 582J582J
  3. Cwork done by the gas is close to 582J582J
  4. Dwork done on the gas is close to 332J332J

Correct answer

B. work done on the gas is close to 582J582J

Step-by-step solution

Since, each vibrational mode, corresponds to two degrees of freedom, hence, f=3(trans.)+3(rot.)+8(vib.)=14f =3 ( trans .) +3( rot . )+8( vib . )=14

 and γ=1+2f\text{ and } \gamma = 1 + \dfrac{2}{f}

γ=1+214=87\gamma = 1 + \dfrac{2}{14} = \dfrac{8}{7}

W=nR\DeltaTγ−1=−582W = \dfrac{nR\DeltaT}{\gamma - 1} = - 582

As W<0W < 0. work is done on the gas.

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