Question

Venus has an average temperature of 460? C. What fraction of CO2

molecules are moving faster than 750 m/s? What percentage of the

molecules are moving faster than the escape velocity of 10.4 km/s? (This

will be a very small percentage...) (b) Answer both of these questions for

H2.

Answer 1

Maxwell Boltzmann velocity distribution is

The fraction of molecules that are moving faster than v_o m/s is

m is the molar mass of the gas.

a) For CO2 substitute

This gives

This integral can be computed numerically as it doesn't have a closed form answer. The answer is

Hence the percentage of CO2 molecules that have speeds faster than 750 m/s on Venus is 25.5 %

10.4 km/s = 10400 m/s

The fraction of molecules that have speeds faster than 10400 m/s on Venus is  

Hence the percentage of CO2 molecules that have speeds greater than 10400 m/son Venus is

b) For hydrogen H2, m = 2 grams = 0.002 kg

For this the fraction of molecules that have speeds above v0 is

The fraction of H2 molecules that have speeds greater than 750 m/s is

Hence the percentage of H2 molecules that have speeds faster than 750 m/s on Venus is 98 %

The fraction of H2 molecules that have speeds faster than 10400 m/s on Venus is  

Hence the percentage of H2 molecules that have speeds faster than 10400 m/s on Venus is