$0.056 \,kg$ of Nitrogen is enclosed in a vessel at a temperature of $127\,^{\circ} C$. The amount of heat required to double the speed of its molecules is k cal. (Take $R =2$ $cal \,mole$ $^{-1} K ^{-1}$ )
A$12$
B$18$
C$17$
D$122$
JEE MAIN 2022, Medium
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A$12$
a $0.056 \,kg N N _{2}=56\, gm$ of $N _{2}=2\, mole$ of $N _{2}$
$T _{1}=400\, K , v \alpha \sqrt{ T }$ so $T _{2}=4 T _{1}=1600\, K$
$Q =\frac{ f }{2} nR \Delta T$
$f=5$
$Q =12 \,k \,cal$
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