Question

Temperature of an ideal gas is changed from $-{173}^{\circ }\text{C}$ to ${127}^{\circ }\text{C}$. Thus the average velocity changes by $x$ times. The value of $x$ is

Answer 1

Average velocity is given by
$u_{avg}=\sqrt{\frac{8RT}{\pi M}}$
$T_1=-173+273=100K$ and $T_2=127+273=400K$, so
$\frac{(u_{avg}{)}_2}{(u_{avg}{)}_1}=\sqrt{\frac{T_2}{T_1}}=\sqrt{\frac{400}{100}}=\sqrt{4}=2$
$(u_{avg}{)}_2=2(u_{avg}{)}_1$
Hence, average velocity changes by 2 times.