About 0.014 kg nitrogen is enclosed in a vessel at temperature of `27^(@)C` How much heat has to be transferred to the gas to double the rms speed of its molecules ? `(R = 2 cal//mol K)`

Explanation

`v_(rms)=sqrt((3RT)/(M_0))`
To double rms speed, the temperature must be made for times.
`T_1=27^@C=300K`,`T_2=4xx300=1200K`
`(DeltaQ)_V=nC_VDeltaT=(0.014xx10^3)/(28)xx(5R)/(2)(T_2-T_1)`
`=(1)/(2)xx(5xx8.3)/(2)(1200-300)`
`=9337.5J`