The temperature at which the r.m.s velocity of a gas triples to its r.m.s. velocity at $0^{\circ}…
The temperature at which the r.m.s velocity of a gas triples to its r.m.s. velocity at $0^{\circ} \mathrm{C}$ is
$2184 \mathrm{~K}$
$2184^{\circ} \mathrm{C}$
$2100^{\circ} \mathrm{C}$
$555 \mathrm{~J}$
Solution
For a gas,
$v_{\mathrm{rms}}=\sqrt{\frac{3 K T}{m}}$ or $v_{\mathrm{rms}} \propto \sqrt{\mathrm{T}}$
Here, $T=$ Temperature in kelvin,
Hence, $\quad \frac{v_T}{v_0}=\sqrt{\frac{T}{0+273}}$
$\Rightarrow$ Given, $V_T=3 \times v_0$
so, $\quad 3=\sqrt{\frac{T}{273}}$
or $\quad T=9 \times 273=2457 \mathrm{~K}$
$\begin{array}{ll}\Rightarrow & T=(2457-273)^{\circ} \mathrm{C} \\ \text { or } & T=2184^{\circ} \mathrm{C}\end{array}$