15.2 Ideal Gas Equation of State

Ideal Gases

An ideal gas is a theoretical gas that perfectly obeys they gas laws under all conditions.

Definition: Ideal Gas

• An ideal gas is a gas which obeys the relationship $pV\propto T$
• For all values of $p$, $V$, and $T$, where $T$ is the thermodynamic temperature.

Equation of State

Macroscopic Form (Using Moles)

$pV=nRT$

Where:

• $p$ : Pressure ($\text{Pa}$)
• $V$ : Volume (${\text{m}}^3$)
• $n$ : Amount of substance ($\text{mol}$)
• $R$ : Molar gas constant ($8.31{\text{ J K}}^{-1}{\text{ mol}}^{-1}$)
• $T$ : Thermodynamic temperature ($\text{K}$)

Microscopic Form (Using Molecules)

$pV=NkT$

Where:

• $p$ : Pressure ($\text{Pa}$)
• $V$ : Volume (${\text{m}}^3$)
• $N$ : Total number of molecules
• $k$ : Boltzmann Constant ($1.38\times 10^{-23}{\text{ J K}}^{-1}$)
• $T$ : Thermodynamic temperature ($\text{K}$)

Boltzmann Constant ( $k$)

$k=\frac{R}{N_A}$