Question

The molecules of a given mass of a gas have a r.m.s. velocity of 200 m/sec at 27°C and $1.0 \times 10^{5}N/m^{2}$ pressure. When the temperature is 127°C and pressure is $0.5 \times 10^{5}N/m^{2}$, the r.m.s. velocity in m/sec will be

• A. $\frac{100\sqrt{2}}{3}$
• B. $100\sqrt{2}$
• C. $\frac{400}{\sqrt{3}}$
• D. None of the above

Answer 1

Answer: (C)

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

Answer 2

r.m.s. velocity doesn't upon pressure, it depends upon temperature only i.e. $v_{rms} \propto \sqrt{T}$

Ž$\frac{v_{1}}{v_{2}} = \sqrt{\frac{T_{1}}{T_{2}}}$Ž$\frac{200}{v_{2}} = \sqrt{\frac{(273 + 27)}{(273 + 127)}} = \sqrt{\frac{300}{400}}$

Ž$v_{2} = \frac{400}{\sqrt{3}}m/\sec$