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:
A
Work done by the gas is close to 332 J
B
Work done on the gas is close to 582 J
C
Work done by the gas is close to 582 J
D
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.
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