Thank you for reporting, we will resolve it shortly
Q.
A vessel contains $14 g$ of nitrogen gas at a temperature of $27^{\circ} C$. The amount of heat to be transferred to the gap to double the r.m.s. speed of its molecules will be :
(Take $R =8.32 J mol ^{-1} k ^{-1}$ )
$ v _{ rms } \propto \sqrt{ T } $
$ v _{ rms } \propto \sqrt{300 K }, v _{ rms _{ f }}=2 v _{ rms _{ i }}$
$ v _{ rms _{ f }} \propto \sqrt{1200 K } $
$ T _{ f }=1200 K , T _{ i }=300 K , n =\frac{14}{28}=\frac{1}{2}$
$ Q = nC _{ v } \Delta T =\frac{1}{2} \times \frac{5 R }{2} \times 900 $
$ Q =9360\, J $