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12.Kinetic Theory of Gases
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The following graph shows two isotherms for a fixed mass of an ideal gas. The ratio of $r.m.s.$ speed of the molecules at temperatures $T_2$ and $T_1$ is

A
$2\sqrt 2 $
B
$\sqrt 2 $
C
$2$
D
$4$
Solution
We know that
$\mathbf{P V}=\mu \mathbf{r R}, \mu, R$ constant
$\mathrm{T}_{1} \propto \mathrm{P}_{1} \mathrm{V}_{1}$ and $\sqrt{2} \propto \mathrm{P}_{2} \mathrm{V}_{2}$
$\mathrm{T}_{1}=1 \times 1$ unit, $\mathrm{T}_{2}=2 \times 2$ unit
$\Rightarrow \mathrm{V}_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$
Standard 11
Physics