Question

If the absolute temperature of a gas is increased 5 times, then the rms velocity of the gas molecules will be ______.

Options

• 5 times

• 25 times

• `sqrt5` times

• 10 times

Answer 1

If the absolute temperature of a gas is increased 5 times, then the rms velocity of the gas molecules will be `underlinebbsqrt5` times.

Explanation:

Roots mean square velocity, v_rms = `sqrt((3RT)/M)`

Initial rms velocity, v_rms ∝ `sqrtT`

suppose, `"v"_{rms_1} = "v"_{rms}` and T₁ = T

`"v"_{rms_2} = ?` and `T_2 = 5T`

∴ `("v"_{rms_2})/(r_{rms_1}) = sqrt(T_2/T_1) = sqrt((5T)/T)` 

∴ `"v"_{rms_2} = sqrt5` v_rms