# 10.2 Ideal Gas Law and Kinetic Theory of Gases

##### Chad's General Physics Master Course

Quizzes, Study Guides, Chapter Tests, Equation Cheat Sheets, and More!

## Ideal Gas Law and the Kinetic Theory of Gases

Gases have no definite shape or volume.
Liquids have a definite volume but no definite shape.
Solids have definite shape and volume.

KINETIC THEORY OF GASES
1. A gas is comprised of a large number of atoms/molecules moving randomly.
2. Gas particles are point-like having negligible volume.
3. Gas molecules do not exert long range forces on one another.
4. All collisions between molecules and with the walls are elastic.

Gases behave more ‘ideally’ at low pressures and high temperatures.

n = N / NA          n = # moles          N = # particles          NA = 6.02 × 1023

m = m / M           n = # moles          m = mass          M = molar mass

GAS LAWS
Boyle’s Law
(constant T)
P ∝ 1 / V          or          PV = constant          or          P1V1 = P2V2
Charles’ Law
(constant P)
V ∝ T          or          V / T = constant          or          V1 / T1 = V2 / T2
(constant T, P)
V ∝ n          or          V / n = constant          or          V1 / n1 = V2 / n2
Gay-Lussac's Law
(constant V)
P ∝ T          or          P / T = constant          or          P1 / T1 = P2 / T2
Ideal Gas Law PV = nRT                 R = 8.31 J / mol • K = 0.0821 L•atm / mol•K
PV = NkBT                 kB = 1.38 × 10-23 J/K
R = NAkB

Kinetic Energy, Internal Energy, Temperature, and Root Mean Square Speed

Maxwell Distribution of Speeds