Question

At what temperature the rms speed of nitrogen will be twice that of zero degree Celsius

Answer 1

The r.m.s. speed of nitrogen molecules depends on the root of their absolute temperature.

Since the initial temperature is 0°C,

$T_{i} = 0°C = 273K$

For the speed to double, due to the square-root variation, the temperature shall have to become 4 times, that is,

$T_{f} = 4T_{i}$

Hence,

$T_{f} = 4 * 273 K = 1092K$