If the absolute temperature of a gas is tripled, what happens to the rootmeansquare speed of the molecules?
1 Answer
It increases by a factor of
Explanation:
The rootmeansquare speed
where

#R# is the universal gas constant, for this case#8.314("kg"·"m"^2)/("s"^2·"mol"·"K")# 
#T# is the absolute temperature of the system, in#"K"# 
#MM# is the molar mass of the gas, in#"kg"/"mol"#
The question is nonspecific for which gas, but we're just asked to find what generally happens to the r.m.s. speed if only the temperature changes, so we'll call the quantity
If the temperature is tripled, then this becomes
To find what happens, let's divide this value by the original equation:
Thus, if the temperature is tripled, the rootmeansquare speed of the gas particles increases by a factor of