The average energy of molecules in the atmosphere, such as nitrogen and oxygen is
proportional to absolute temperature:!
!
is the average translation kinetic energy!
R is the gas constant 8.314 !
is Avagadro’s number!
T is temperature in Kelvins!
The average kinetic energy of the gas is given by the average speed of its particles or root
mean square speed:!
!
Where !
!
And M is molar mass in kg/mol!
We want in the case of the Earth that!
!
For the earth to hold its atmosphere. Thus it would vaporize at a temperature of!
!
Where !
!
!
The planet mercury, the closest to the sun is 800F in the day. Thus the earth needs to be 131
times hotter than that for its atmosphere to vaporize.!
Click here to go to the homepage: https://eanbardsley.github.io/source/index.html
e
k
=
3
2
R
N
a
T
e
k
kg * m
2
/s
2
* mol * K
N
A
e
k
=
1
2
m ¯u
2
¯u =
3RT
M
¯u < v
e
T =
Mv
e
2
3R
= 58,611K = 58,338C = 105,040F
v
e
= 7100m /s
M = 0.029kg/m ol
