Question

$0.056\, kg$ 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 $^{-1} \,K ^{-1}$ )

Answer 1

$0.056 \,kg \,N _{2}=56 \, gm$ of $N _{2}=2$ mole of $N _{2}$
$T _{1}=400 \,K , v \alpha \sqrt{ T }$ so $T _{2}=4 T _{1}=1600 \, K$
$Q =\frac{ f }{2} nR \Delta T$
$f =5$
$Q =12 \, k \, cal$