One mole of an ideal gas is taken through an adiabatic process where… | JEE Main 2021 (27 Jul, Shift 2)

Q190JEE Main 2021 · 27 JUL · SHIFT 2Medium

Thermodynamic Processes

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

Show answer and solution

Answer: (b)

Degrees of freedom: 3 translational + 3 rotational + $2\times4$ vibrational $= 14$ , so $C_v = \frac{14}{2}R = 7R$ .
Adiabatic: $Q = 0$ , so $W_{on} = \Delta U = nC_v\Delta T$ .
$\Delta U = 1 \times 7 \times 8.314 \times 10 \approx 582$ J (positive, temperature rises, so work is done on the gas).
So the answer is (b) work done on the gas is close to 582 J.

Report a mistake

More questions on Thermodynamic Processes

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is…JEE Main 2021 (18 Mar, Shift 2)
A sample of gas with γ = 1.5 is taken through an adiabatic process in which the volume is…JEE Main 2021 (31 Aug, Shift 2)
An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a…MHT CET 2021 (24 Sep, Shift 1)
The initial pressure and volume of a gas is ' P ' and ' V ' respectively. First by…MHT CET 2021 (23 Sep, Shift 2)
A monoatomic gas at pressure ' P ' having volume ' V ' expands isothermally to a volume 2…MHT CET 2021 (21 Sep, Shift 1)
1 mole of rigid diatomic gas performs a work of Q/5 when heat Q is supplied to it. The…JEE Main 2021 (26 Feb, Shift 2)
The volume V of a given mass of monoatomic gas changes with temperature T according to…JEE Main 2021 (26 Feb, Shift 2)
In a certain thermodynamical process, the pressure of a gas depends on its volume as kV3…JEE Main 2021 (25 Feb, Shift 1)

Thermodynamic Processes question from JEE Main 2021 (27 Jul, Shift 2)

More questions on Thermodynamic Processes