The equation that relates the pressure P, temperature T and volume V of a gas is called the equation-of-state. In general, the equation-of-state of a gas is complicated. In the limit of low pressure (i.e., low density), the equation-of-state of all gases approach that of the ideal gas.

**Ideal Gas**

Modelling the behavior of a gas as a collection of particles that obey the laws of classical mechanics.

*Assumptions:*

– The gas consists of a large number of identical particles that are on average separated by large distances compared with their dimensions. Thus, the particles occupy a negligible fraction of the volume within the container.

– The particles are in a state of random motion and obey Newton’s laws of motion.

– Collisions between the particles themselves and between the particles and the wall of the container are elastic and of negligible duration.

– No long-range forces act on the particles, only short-range repulsive forces act during collisions.

**The equation-of state of an ideal gas is found to be:**

PV = nRT

,where

P = pressure

V = volume

T = absolute temperature

n = no. of moles of gas (= mass/molar mass)

R = universal gas constant (8.314 J mol^{-1} K^{-1}

Note: Mole is a counting unit, where one mole = 6.022 x 10^{23} particles.

P, V, and T are the thermodynamic variables of the gas.

The behaviour of real gases at not-too-high pressures and at not-too-low temperature is very well described by this ideal gas equation.

**Another form of ideal gas law**

The ideal gas law can also be expressed in number of gas particles N (instead of the number of moles of gas particles n).

PV = Nk_{B}T

,where

P = pressure

V = volume

T = absolute temperature

N = number of gas molecules (i.e., number of molecules)

k_{B} = Boltzmann’s constant (1.381 x 10^{-23} J K^{-1}

Note:

R = N_{A}k_{B}, where N_{A} is the Avogadro’s constant (6.022 x 10^{23})

Next: Concept Of Kinetic Temperature