The average speed of molecules in an ideal gas is ^-u=4/√π(M/2RT)^3/2 ^∞∫0 v^3e^-Mv^2/(2RT) dv where M is the molecular weight of the gas, R is the gas constant, T

is the gas temperature, and is the molecular speed.

Show that −v=√8RT/πM

is the gas temperature, and is the molecular speed.

Show that −v=√8RT/πM