Practice portal › Kinetic Theory of Gases › Speed, Temperature and Molar Mass

The root mean square velocity of molecules of a gas is

Asked in JEE Main 25th Jan 1st Shift 2023 · Speed with temperature and molar mass

(1) Inversely proportional to the square root of temperature (1/(√T))
(2) Proportional to the square root of temperature (√T)
(3) Proportional to the square of temperature (T²)
(4) Proportional to temperature (T)

Answer: (2) Proportional to the square root of temperature (√T)

Step-by-step solution

vᵣₘₛ=√(3RT)/M.

For a given gas M is fixed, so vᵣₘₛ∝√T.

Quadrupling the absolute temperature doubles the rms speed.

Why the other options are wrong

(1) Has the dependence upside down; heating a gas speeds its molecules up.
(3) T² would mean the speed grows far faster than it does; v², not v, is linear in T.
(4) Comes from reading v²∝ T as v∝ T, dropping the square root.

More Speed, Temperature and Molar Mass questions

All Speed, Temperature and Molar Mass questions →

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.

Practise this with a timer