Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main

Exam: JEE Main
Subject: Physics
Chapter: Kinetic Theory of Gases

JEE Main · Physics · Kinetic Theory of Gases

An ideal diatomic gas with& C _ v = (5R)/(2) occupies a volume V _...

An ideal diatomic gas with&

{C}_{v} = \dfrac{5R}{2}

occupies a volume

{V}_{1}

at a pressure

{P}_{1}

. The gas undergoes a process in which the pressure is proportional to the volume. At the end of process the

r

ms speed of the gas molecules has doubled from its initial value then the heat supplied to the gas in the given process is

Options

A $7{P}_{1}{V}_{1}$
B $8{P}_{1}{V}_{1}$
C $9{P}_{1}{V}_{1}$
D $10{P}_{1}{V}_{1}$

Correct answer

C. $9{P}_{1}{V}_{1}$

Step-by-step solution

As

P ∝ V

∴ PV^{- 1} = constant

Also,

C = {C}_{v} - \dfrac{R}{x - 1} = \dfrac{5}{2}R - \dfrac{R}{- 1 - 1} = 3R

But as

r

ms speed is doubled therefore temperature becomes four times.

Hence,

Q = nc ∆ T = n \times 3R \times 3{T}_{1} = 9nR{T}_{i}

= 9{P}_{1}{V}_{1}

Practice Kinetic Theory of Gases on Quantrex Academy →

More from Kinetic Theory of Gases

If 2 mole of an ideal monoatomic gas at temperature T , is mixed with 6 mole of another… JEE Main 2026 Given below are two statements: one is labelled as Assertion A and the other is labelled… JEE Main 2026 Given below are two statements: one is labelled as Assertion A and the other is labelled… JEE Main 2026 One gas of n_1 mole of molecules at temperature T_1 , volume V_1 , and pressure P_1 , and… JEE Main 2026 A mixture of carbon dioxide and oxygen has volume 8310 cm ^3 , temperature 300 K… JEE Main 2026 The mean free path of a molecule of diameter 5 × 10^ -10 ~m at the temperature 41^ ∘ C… JEE Main 2026 A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has… JEE Main 2026 Consider two boxes containing ideal gases A and B such that their temperatures, pressures… JEE Main 2026 Full Kinetic Theory of Gases list All Highly selective Backlog Qs for JEE Main PYQs