Q 11-12-099JEE MainJEE Main 2021 (27 Jul, Shift 2)Medium
One mole of an ideal gas is taken through an adiabatic process where the temperature rises from $27^\circ\text{C}$ to $37^\circ\text{C}$. If the ideal gas is composed of polyatomic molecule that has $4$ vibrational modes, which of the following is true? $[R = 8.314\ \text{J mol}^{-1}\text{K}^{-1}]$
Answer: (B) work done on the gas is close to $582$ J
Degrees of freedom: $3$ translational $+ 3$ rotational $+ 2\times4$ vibrational $= 14$, so $C_V = \dfrac{14}{2}R = 7R$.
$\Delta U = nC_V\Delta T = 7\times8.314\times10 \approx 582$ J.
Adiabatic: $Q = 0$, so $W_{\text{on gas}} = \Delta U \approx 582$ J (temperature rises, so work is done on the gas).
Solution by Sreeraj P, M.Sc Physics