By what factor must the absolute temperature of a gas be increased to increase the rms speed of its molecules by a factor of 3?

The temperature of the molecule will be increased by a factor of 9

Explanation:

The relationship between the temperature and the rms speed of a gas is given by

Vrms=√ (3RT/MM)

Where R = Universal gas constant

T = Absolute temperature of the gas in kelvin

MM = Molar mass of the gas

Since from the question, only the rms speed and the temperature are said to change, the term 3R/MM can be represented by a constant k. The relationship then becomes Vrms=√kT

At the intitial speed, temperature = T1

Vrms=√ (kT1) (1)

When the speed is increased by a factor of 3, the relationship becomes

(3V) rms=√ (kT2) (2)

Dividing equation (2) by equation (1)

(3V) rms/Vrms = √ (kT2) / √ (kT1)

3=√ (T2/T1)

T2/T1 = 9

The temperature of the molecule will be increased by a factor of 9