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 of the following is true? $[\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}]$

(B) Work done on the gas in close to 582 J

(A) Work done by the gas is close to 582 J

(C) Work done on the gas is close to 332 J

(D) Work done by the gas is close to 332 J

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Heat & Thermodynamics

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from

2 7^{\circ} C

3 7^{\circ} C

. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following of the following is true?

[R = 8.314 J mol^{- 1} K^{- 1}]

Answer: (B)

A polyatomic molecule with

4

vibrational modes has

f = 3 + 3 + 2 \times 4 = 14

degrees of freedom, since each vibrational mode carries both kinetic and potential energy. Hence

C_{V} = \frac{f}{2} R = 7 R

. No heat enters or leaves in an adiabatic change, so the work done by the gas is

W = - Δ U = - n C_{V} Δ T = - 1 \times 7 \times 8.314 \times 10 = - 582 J

The temperature rises, so the gas is compressed and the work done on the gas is close to

582

JEE Main · 2021 · 27 Jul 2021 · Shift 2 · Single correct option