First slide

Rms speed

Question

When the temperature of a gas is raised from $27^{0} C to 90^{0} C$ , the percentage increase in the rms velocity of the molecules will be

Moderate

A

10 %
B

15 %
C

20 %
D

17.5 %

Solution

$\frac{C^{'}}{C} = \sqrt{\frac{273 + 90}{273 + 27}} = \sqrt{\frac{363}{300}}$
or $\frac{C^{'}}{C} = \sqrt{1.21} = 1.1$
or $\frac{C^{'}}{C} - 1 = 0.1$
or $\frac{C^{'} - C}{C} \times 100 = 0.1 \times 100 = 10$ %

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