Thermodynamics

JEE Main level, single correct, medium

121 of 190

Question 121 of 190

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27∘C27^{\circ}C to 37∘C37^{\circ}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]

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Answer: (B) work done on the gas is close to 582J582J

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
&\gamma =1+\dfrac{2}{f}
γ=1+214=87\gamma =1+\dfrac{2}{14}=\dfrac{8}{7}
W=nRΔTγ−1=−582W=\dfrac{nR\Delta T}{\gamma -1}=-582
As W<0W\lt 0. work is done on the gas.

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