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

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