First slide

Kinetic theory of ideal gases

Question

The molecules of a given mass of a gas have RMS speed $200 m s^{- 1}$ at 27 ºC and 10 $N m^{- 2}$ pressure. When the absolute temperature is doubled and the pressure is halved, then find RMS speed of the molecules of the same gas $(i n m s^{- 1})$ .

Moderate

A

$100 \sqrt{2}$
B

$200 \sqrt{2}$
C

$400 \sqrt{2}$
D

$400$

Solution

$v_{R M S} = \sqrt{\frac{3 R T}{M}}$ (independent of pressure, for a given temperature).
$\Rightarrow v_{R M S} α \sqrt{T} \frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{2 T_{1}}{T_{1}}} = \sqrt{2} v_{2} = 200 \sqrt{2} m / s$ .

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