Question

What is the ratio of the probability of finding a molecule moving with the average speed to the probability of finding a molecule moving with three times the average speed? How does this ratio depend on the temperature?

Answer 1

Given that V₁ = 3V₂
exp ( -mv² / 2RT) = probability
v = (8RT / πm )^1/2
substitute v in the first expression
f(v₁) / f(v₂) = 3 exp ( - m ((8RT / πm )^1/2)² ) / 2RT
velocity probability of a molecule = f(v₁) / f(v₂) = 3 exp(-8mv*1/2RT)
By increasing the temprature, the velocity probability of a molecule with higher velocity will increase.
Probability of finding a molecule moving with three times the average velocity will increase with an increase in temperature.