1.
Pressure equals force per unit areaDerivation of Ideal Gas Laws
1. Pressure equals force per unit area
2. 
Acceleration equals change in velocity with time
3. 
momentum equals mass times velocity
4. Taking the first derivative of momentum vs. time
or 
5. 
or 
Substituting (4) into (1)
6. Consider the collisions as being 
to the walls of the container
component of velocity to A (area)
7. 
8. Consider these individual molecules of mass (m) in a box with sides
length (L) and velocity conponents in three dimensions.
9. Assume perfectly elestic collisions - What is the change in momentum when a particle
strikes the walls.
10. How long will it be till this same particle strikes this wall again?
Distance = 2 L
or 
then substituting for d gives you 
Collisional frequency = 
11. 
12. Total pressure consider (N) particles
Since the mass of each particle is the same
13. Total Pressure
14. Consider the randomness - the average velocities in each direction
should be the same. i.e. 
15. L3 = V therefore 
16. Ideal gas law : 
compare (15) to (16)
Note: 
or 
Boltzmann constant (k)
17. 
Temperature is proportional to the average KE of a
system
or 
18. 
or 
19. 
substitute in (16) 
This is the average KE per molecule.
Boltzmann constant is 
Therefore, 
20. Total 
( Total translational KE for 1 mole of
a gas at room temperature.)
21. 
velocity of individual molecules at a given T