Question

The molecules of a given mass of gas have a root mean square velocity of $200m.s^{-1}$ at ${27}^{0}C$ and $1.0\times {10}^{5}N.m^{-2}$ pressure. When the temperature is ${127}^{0}C$ and the pressure $0.5\times {10}^{5}N{m}^{-2}$, the root mean square velocity is $m{s}^{-1}$, is

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

Answer 1

The correct option is A $\frac{400}{\sqrt{3}}$

$\frac{C_2}{C_1}$ $=\sqrt{\frac{400}{300}}$
$=\frac{2}{\sqrt{3}}$ $\Rightarrow$ $C_2$
$=\frac{2}{\sqrt{3}}\times 200$
$=\frac{400}{\sqrt{3}}m{s}^{-1}$