# What will be the temperature when the rms velocity is double of that at 300k?

Arun
25758 Points
2 years ago

$V_{rms} = \sqrt{\frac{3RT}{M}}$

$\Rightarrow V_{rms}\ \propto\ \sqrt{T}$

$V_{rms}$  will be doubled when temperature increases four times.

$\therefore$  Temperature = 4 $\times$ initial temperature

= 1200 K

Hope it helps

Khimraj
3007 Points
2 years ago

Let the initial and final velocities be u and v respectively.

Since v and u are propotional to √T

v/u = √T(final)/√T(initial) = 2

Squaring on both sides, 4=T(final)/T(initial)

T(initial) = 300 K

Therefore T(final) = 4 × 300 = 1200 K