AP PHYSICS 2
SUMMARY CHAPTER 9 – GASES
PROPERTIES OF AN IDEAL GAS:
1. There is large number of Particles moving in random directions with a variety of speeds. They do not
have the same speed of kinetic energy, but their average kinetic energy will depend on temperature.
2. The molecules are very tiny compared to the average distance between them. In a true ideal gas, the
molecules would have zero radius.
3. The molecules obey Newton’s Laws of motion. They only interact when they collide, there is no “long
distance” interaction between particles.
4. The collisions between molecules and with the wall of the container are perfectly elastic, so that kinetic
energy is not lost.
CONSTANT NUMBERS:

Avogadro’s Number
𝑁𝐴 =

Boltzmann’s constant
𝑘=

Universal Gas constant
𝑅=
6.023 x 1023 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠
mole
1.38x10−23 𝐽
degree.
8.3 𝐽
K ∙ mole
MATHEMATICAL MODELS


Pressure
Density
F
P=
A
ρ=


1 ̅̅̅2
2 N (2 mv )
P= [
]
3
V
m
V
Average kinetic energy
3kT
̅̅̅̅=
KE
2
3PV
2N
N = number of molecules
n = number of moles
PV = NkT
PV = nRT
̅̅̅̅
KE=


Ideal gas model
̅̅̅̅
2N𝐾𝐸
3
Thermal energy
PV=

3kT
Uthermal =N (
N = n  NA
M = Molar mass (mass of one mole)
MP = mass of one particle
𝑚𝑃 =
𝑀
𝑁𝐴

)
3𝑃𝑉
2
Conversions of Temperature
9
𝑇𝐹 = 𝑇𝐶 + 320
5
5
𝑇𝐶 = (𝑇𝐹 − 320 )
9
𝑇𝐾 = 𝑇𝐶 + 273.150
Uthermal =


2
Root mean square speed of a gas molecule:

𝟑𝒌𝑻
𝒗𝒓𝒎𝒔 = √
𝒎
Constant pressure (isobaric) process. A container with a frictionless plunger is
filled with gas. The air outside is at constant pressure thus the pressure inside the
container is constant.
 Microscopic: The molecules inside collide with container walls at different
speeds and varying frequency. If gas warms, the particles collide harder and
more often, thus causing the gas to expand.
Charles’s Law:
Assume that N, n, and P are constant.
Then,
𝑉1 𝑉2
=
𝑇1 𝑇2

Constant volume (isochoric) process. A closed oxygen tank sits outside on a
sunny summer day. Its volume is constant.
 Microscopic: As a gas warms, the molecules inside move faster and collide
with walls more often, thus exerting greater pressure on walls.
Gay-Lussac’s Law:
Assume that N, n, and V are constant.
Then,
𝑃1 𝑃2
=
𝑇1 𝑇2

Constant temperature (isothermal) process. A plastic bottle shrinks as an
airplane descends. The temperature inside the bottle is always equal to the
temperature outside.
 Microscopic: As pressure increases, the collisions of air molecules against
the outside of the bottle become more frequent, causing. The bottle volume
to decrease.
Boyle’s Law:
Assume that N, n, and T are constant.
Then,
𝑃1 𝑉1 = 𝑃2 𝑉2