Gas pressure and the ideal gas law
Assume specular collisions*
Change in momentum:
mv cos    mv cos  
 2mv cos 
*Bold assumption – but more general calculation gives same result.
Molecular Flux
Element of area on the wall
of the container where
molecules exert a pressure
due to their change in
momentum upon bouncing
from the wall. In time dt ,
molecules traveling at angle
 will each sweep out a
volume vdtcosdA.
# of molecules
n
volume
Gas pressure and the ideal gas law
Kinetic theory provides a natural interpretation of the
absolute temperature of a dilute gas. Namely, the
temperature is proportional to the mean kinetic energy (e )
of the gas molecules.
•
The mean kinetic energy is independent of pressure,
volume, and the molecular species, i.e. it is the same for
all molecules.
1
2
1 2 2
2
PV  Nmv   N  mv   N e  NkT
3
3
2
 3