1. The Three Gas Laws pV = constant V/T = constant
Unit 4: Module 3 – Thermal Physics
The Three Gas Laws
Boyle’s Law states:
At a constant temperature, the pressure of a gas is inversely proportional to its volume.
pV = constant
Charles’ Law states:
At a constant pressure, the volume of a gas is directly proportional to its absolute temperature.
V/T = constant

2. The Three Gas Laws Cont. p/T = constant
Unit 4: Module 3 – Thermal Physics
The Three Gas Laws Cont.
The Pressure Law states:
At a constant volume, the pressure of a gas is directly proportional to its absolute temperature.
p/T = constant
Each of these laws were worked out independently by careful experiment. Each law applies to a fixed mass of gas. Ideal gases obey these laws.

3. The Ideal Gas Equation pV/T = nR pV = nRT (ideal gas equation)
Unit 4: Module 3 – Thermal Physics
The Ideal Gas Equation
Combining all 3 gas laws gives us: pV/T = constant
The constant depends on how much gas is present, therefore for n moles of gas:
pV/T = nR
Where R is the molar gas constant = 8.31 J mol-1K-1
Rearranging gives:
pV = nRT (ideal gas equation)

4. One mole of any substance contains 6.02 x 1023 particles.
Unit 4: Module 3 – Thermal Physics
The Mole
One mole of any substance contains 6.02 x 1023 particles.
Avogadro’s Law
Equal volumes of gases under conditions of equal temperature and pressure contain the same number of molecules.
Avogadro Constant
The Avogadro constant NA is 6.02 x 1023 mol -1

5. Don’t get confused with all the n’s.
Unit 4: Module 3 – Thermal Physics
Which N ?
Don’t get confused with all the n’s.
The number of particles in a mass of gas, N = number of moles n x Avogadro’s number NA.

6. Boltzmann’s constant, k
Unit 4: Module 3 – Thermal Physics
Boltzmann’s constant, k
If R (molar gas constant) is the gas constant for one mole of gas.
k (Boltzmann’s constant) is the gas constant for one particle of gas.
k = R/NA and k =1.38 x JK-1
from pV = nRT
pV = NkT (The equation of state)

7. Kinetic Energy of a gas Molecule
Unit 4: Module 3 – Thermal Physics
Kinetic Energy of a gas Molecule
We now know: pV = 1 Nm <c2> and pV = nRT 3
If we equate both (for 1 mole of gas):
1 NAm <c2> = RT
(rearrange and multiply both sides by ½)
We get: 1 m<c2> = 3RT Where K =R
NA NA
K = Boltzmann constant (JK-1)
As 1 m<c2> = Mean Kinetic Energy of a gas molecule 2
Ek = 3 KT Where Ek = kinetic energy
K = Boltzmann Constant
T = Kelvin temperature