First slide

Rms speed

Question

The molecules of a given mass of a gas have r.m.s. velocity of $200 m s^{- 1}$ at $27 ° C$ and $1.0 \times 10^{5} N m^{- 2}$ pressure. When the
temperature and pressure of the gas are respectively, $127 ° C$ and $0.05 \times 10^{5} N m^{- 2}$ the r.m.s. velocity of its molecules in $m s^{- 1}$

Moderate

A

$\frac{100 \sqrt{2}}{3} m s^{- 1}$
B

$\frac{100}{3} m s^{- 1}$
C

$100 \sqrt{2} m s^{- 1}$
D

$\frac{400}{\sqrt{3}} m s^{- 1}$

Solution

$As, v_{rms} = \sqrt{\frac{3 k_{B} T}{m}}$
$∴ \frac{v_{27}}{v_{127}} = \sqrt{\frac{27 + 273}{127 + 273}} = \sqrt{\frac{300}{400}} = \frac{\sqrt{3}}{2}$
$or v_{127} = \frac{2}{\sqrt{3}} \times v_{27} = \frac{2}{\sqrt{3}} \times 200 m s^{- 1} = \frac{400}{\sqrt{3}} m s^{- 1}$

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