The molecules of a given mass of gas have a root mean square velocity of 200 m s^ -1 at 27^ ^ C and 1.0 × 10^ 5 Nm^ -2 pressure. When the temperature is 127^ ^ C and the pressure 0.5 × 10^ 5 Nm^ -2 , the root mean

Correct answer: A. 400 3 c_ 2 c_ 1 = (400)/(300) = 2 3 c_ 2 = 2 3 ×200= 400 3 ms^ -1

BITSAT 2011

BITSAT 2011 · Physics · Kinetic Theory of Gases

The molecules of a given mass of gas have a root mean square...

The molecules of a given mass of gas have a root mean square velocity of

200 \mathrm{ m} \mathrm{ s}^{-1}

27^{{}^{\circ}} \mathrm{C}

and

1.0 \times 10^{5} \mathrm{Nm}^{-2}

pressure. When the temperature is

127^{{}^{\circ}} \mathrm{C}

and the pressure

0.5 \times 10^{5} \mathrm{Nm}^{-2},

the root mean square velocity in

\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm\mathrm{ms}^{-1}

, 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}} \times200=\frac{400}{\sqrt{3}} \mathrm{ ms}^{-1}