The Ideal Gas
For a lowdensity/hightemperature gas,
we neglect the longrange intermolecular attraction and treat the shortrange
repulsion as perfect elastic. This leads to:
The Ideal Gas Model
 The gas consists of a large number of identical
molecules (for air, density ≈
10^{25} molecules/m^{3}).
 The volume occupied by molecules themselves is negligible compared to the volume of the container
(molecular volume ≈ 10^{29}
m^{3}).
 Molecules move at constant speed in random
directions between collisions (typical speed
550 m/s).
 Molecules experience forces only during collisions that are elastic and instantaneous
(typical time between collisions 10^{11} sec).
An easytoremember number:
ρ_{air} ≈ ρ_{water}/1000.
Ideal Gas Law:
P V = n R T
where P is pressure, V is volume, n is the number of moles, T is the
absolute temperature, and R = 8.31 J/(mol K) is the universal gas constant.
This can be written in terms of N, the number of molecules, instead.
Using N = nN_{A}, where N_{A} is Avogadro's number, we obtain:
PV = nN_{A} 
R
 
N_{A}


T = N k T 
where the Boltzmann constant k = 1.38 x 10^{23} J/K is the
universal gas constant divided by Avogadro's number.
Intuition for the Ideal Gas Law:
 The pressure of an ideal gas is proportional to
1/V squeezing a gas leads to higher pressure.
 Pressure is caused by molecules colliding with the container walls.
This leads to P ∝ T . As T
→ 0, the thermal energy → 0. Then there are no collisions with
container walls and therefore no pressure.