At what temperature, the rms velocity of gas shown at 50⁰C will be doubled

Options

(a) 626 K
(b) 1019 K
(c) 200⁰C
(d) 1019⁰C

Correct Answer:

1019⁰C

Explanation:

C(rms) = √(3RT / M)
Where T is in Kelvin scale.
For rms velocity to be doubled, T in Kelvin scale must be raised 4 times. So it should be
4 × (50 + 273) = 1292 K = 1292 – 273 = 1019⁰C