One mole of an ideal gas|KTG & THERMODYNAMICS| JEE-Main 2021

JEE MAIN 2021

27-07-2021 S2

Question

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

Select the correct option:

Work done by the gas is close to 332 J

Work done on the gas is close to 582 J

Work done by the gas is close to 582 J

Work done on the gas is close to 332 J

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

Since, each vibrational mode, corresponds to two degrees of freedom, hence, $\mathrm{f}=3$ (trans.) +3 (rot.) +8 (vib.) $=14$ \& $$ \begin{aligned} & \gamma=1+\frac{2}{f} \\ & \gamma=1+\frac{2}{14}=\frac{8}{7} \end{aligned} $$ $$ \mathrm{W}=\frac{\mathrm{nR} \Delta \mathrm{~T}}{\gamma-1}=-582 $$ As $\mathrm{W}<0$. work is done on the gas.

Question Tags

JEE Main

Physics

Easy

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