# softmatter:Ideal Gas

An ideal gas is a hypothetical gas consisting of particles of zero volume that experience no intermolecular forces, but undergo elastic collisions with the walls.

## Ideal Gas Law

### Thermodynamic treatment

Formulated by Clapeyron, the ideal gas law can be expressed as:

PV = nRT

where, P is pressure, V is volume, n is the amount of material (mol or lb-mol), R is the gas constant and T is the temperature. For various units, R has the value of:

Gas constant R (Units)
8.314472 meter3·Pascal·Kelvin-1·mol-1
0.08205784 Liter·atm·Kelvin-1·mol-1
62.3637 Liters·mmHg·Kelvin-1·mol-1
10.7316 ft3·psi·°Rankin-1·lb-mol-1

### Statistical Mechanics treatment

Additionally, the gas law can be expressed in terms of the number of atoms/molecules:

PV = NkT

where P, V, and T are unchanged, but now N corresponds to the number of atoms/molcules, and k is the Boltzmann constant. The Boltzmann constant has the following values for various units:

Boltzmann constant k (Units)
1.380 6504x10-23 Joules/Kelvin
8.617 343x10-5 electron-volt/Kelvin
1.3807x10-16 erg/Kelvin