Answer:
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
