Question

The molecules of a given mass of a gas have arms velocity of 200 m/sec at 27⁰C 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 rms velocity in m/sec will be

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

Answer 1

Answer: (C)

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

Answer 2

Change in pressure will not affect the rms velocity of molecules. So we will calculate only the effect of temperature.

As $v_{rms} \propto \sqrt{T}$

∴ $\frac{v_{300^{o}}}{v_{400^{o}}} = \sqrt{\frac{300}{400}} = \sqrt{\frac{3}{4}}$

⇒ $\frac{200}{v_{400}} = \sqrt{\frac{3}{4}}$ ⇒ $v_{400} = \frac{200 \times 2}{\sqrt{3}} = \frac{400}{\sqrt{3}}m ⥂ / ⥂ s$.