The temperature of an ideal gas is increases from 120 K to 480 K. if at 120 K the root mean square velocity…

Q: The temperature of an ideal gas is increases from 120 K to 480 K. if at 120 K the root mean square velocity of the gas molecules is v. at 480 K it becomes

(a) 4 v

(b) 2 v

(c) v/2

(d) v/4

Ans: (b)

Sol: $\large v_{rms} = \sqrt{\frac{3RT}{M}}$

$\large v_{rms} \propto \sqrt{T}$

Here , temperature becomes 4 times , hence RMS speed becomes 2 times i.e. 2 v .