First slide

Rms speed

Question

The molecules ofa given mass of a gas have a rms velocity of 200 m,/sec at $27^{0} C and 1.0 x 10^{5} N / m^{2}$ pressure. When the temperature is $127^{0} C and pressure is 0.5 x 10^{5} N / m^{2}$ , the rms velocity in m./sec will be

Easy

A

$\frac{100 \sqrt{2}}{3}$
B

$100 \sqrt{2}$
C

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

None of these

Solution

Change in pressure will not affect the rms velocity of molecules. So we will calculate only the effect of temperafure.
$As v_{rms} \propto \sqrt{T}$
$∴ \frac{v_{300^{0}}}{v_{400^{0}}} = \sqrt{\frac{300}{400}} = \sqrt{\frac{3}{4}} \Rightarrow \frac{200}{v_{400}} = \sqrt{\frac{3}{4}}$
$\Rightarrow v_{400} = \frac{200 \times 2}{\sqrt{3}} = \frac{400}{\sqrt{3}} m / s$

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