Question

The molecules of a given mass of a gas have r.m.s. velocity of $200m{s}^{-1}$ at ${27}^{\circ }C$ and $1.0\times {10}^{-5}N{m}^{-2}$ pressure. When the temperature and pressure of the gas are respectively, ${127}^{\circ }C$ and $0.05\times {10}^{5}N{m}^{-2}$, the r.m.s. velocity of its molecules in $m{s}^{-1}$ is :

• A. $100\sqrt{2}$
• B. $\frac{400}{\sqrt{3}}$
• C. $\frac{100\sqrt{2}}{3}$
• D. $\frac{100}{3}$

Answer 1

Answer: (B)

$\frac{400}{\sqrt{3}}$

Here $v_1=200m/s$

temperature $T_1={27}^{\circ }C=27+273=300K$

temperature $T_2={127}^{\circ }C=127+273=400K,V=?$

R.M.S. Velocity, $V\propto \sqrt{T}$

$\Rightarrow \frac{v}{200}=\sqrt{\frac{400}{300}}$

$\Rightarrow v=\frac{200\times 2}{\sqrt{3}}m/s$

$\Rightarrow v=\frac{400}{\sqrt{3}}m/s$.