The Ideal Gas
For a low-density/high-temperature gas,
we neglect the long-range intermolecular attraction and treat the short-range
repulsion as perfect elastic. This leads to:
The Ideal Gas Model
- The gas consists of a large number of identical
molecules (for air, density ≈
- The volume occupied by molecules themselves is negligible compared to the volume of the container
(molecular volume ≈ 10-29
- Molecules move at constant speed in random
directions between collisions (typical speed
- Molecules experience forces only during collisions that are elastic and instantaneous
(typical time between collisions 10-11 sec).
An easy-to-remember number:
ρair ≈ ρwater/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 = nNA, where NA is Avogadro's number, we obtain:
|PV = nNA
|| 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.