Question

The escape speed from the Earth is 1.12×104m/s, so that a gas molecule travelling away from Earth near the outer boundary of the Earth's atmosphere would, at this speed, be able to escape from the Earth's gravitational field and be lost to the atmosphere.

Part A At what temperature is the average speed of oxygen molecules equal to 1.12×10^4m/s? Part B At what temperature is the average speed of helium atoms equal to 1.12×10^4m/s?

Answer 1

We know that average speed of the gas molecules

part A) here , R=8.314 J/mol K , M=32 g/mol =32*10^-3 kg/mol

put these value in above equation

T=(1.12*10⁴)²*3.14*32*10^-3/8*8.314

T=1.895*10⁵ K answer

part B) M= 4 g/mol =4*10^-3 kg/mol   

so T=(1.12*10⁴)²3.14*4*10^-3/8*8.314

T=0.237*10⁵

T=2.37*10⁴ K answer