First slide

Kinetic theory of ideal gases

Question

When the temperature of a gas is raised from 27°C to 90°C, the percentage increase in the r.m.s. velocity of the molecules will be

Moderate

A

10%
B

15%
C

20%
D

17.5%

Solution

$\begin{array}{l} v_{rms} = \sqrt{\frac{3 RT}{M}} \Rightarrow \frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} = \sqrt{\frac{(273 + 90)}{(273 + 30)}} = 1 .1 \\ % increase = (\frac{v_{2}}{v_{1}} - 1) \times 100 = 0 .1 \times 100 = 10 % \end{array}$

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