The equation of state is a simple rule that tells us how a gas behaves when we change its pressure, volume or temperature.
For an ideal gas the rule is: \$PV = nRT\$
Think of a gas as a classroom full of students.
The gas constant R is like the total energy that one mole of students would bring to the classroom.
The Boltzmann constant k is the energy contribution of just one student.
The relationship between them is: \$k = \dfrac{R}{N_A}\$
where \$N_A\$ is Avogadro’s number – the number of students in one mole.
| Constant | Symbol | Value | Units |
|---|---|---|---|
| Universal Gas Constant | \$R\$ | 8.314 | J mol⁻¹ K⁻¹ |
| Avogadro’s Number | \$N_A\$ | 6.022 × 10²³ | mol⁻¹ |
| Boltzmann Constant | \$k\$ | 1.381 × 10⁻²³ | J K⁻¹ |
Using the values above:
\$k = \frac{R}{N_A} = \frac{8.314\ \text{J mol}^{-1}\text{K}^{-1}}{6.022\times10^{23}\ \text{mol}^{-1}} \approx 1.38\times10^{-23}\ \text{J K}^{-1}\$
So each molecule carries about \(1.38\times10^{-23}\) joules of energy per kelvin.
Understanding the equation of state helps you predict how a gas will react when you heat it, compress it, or change its amount.
It’s the foundation for topics like thermodynamics, kinetic theory, and real‑gas behaviour.
Remember: pressure, volume, temperature, and amount of substance are all connected.