# Ideal Gas and it’s importance

Most of the thermodynamic relations are valid under certain conditions , like

PV¥ = constant , valid only for reversible adiabatic process

Similarly ,

∆W = mRT1 ln ( V2 / V1 ) , valid only for

• closed system
• Reversible process
• Ideal gas

Therefore it becomes important to know about these parameters in Thermodynamics .

## What is ideal gas?

Ideal gas is the gas for which –

(a) The intermolecular forces i.e., molecular attraction and molecular repulsion forces are negligible.

(b) Volume occupied by the molecule becomes negligible compared to the container volume.

(c) all gas laws are followed in all conditions

(d) temperature remains high and pressure low.

At low pressure and high temperature all the gas start to behave as ideal gas.

##### Example of ideal gas :

In reality no gas is ideal gas , but under certain conditions ( high temperature and low pressure ) real gases like nitrogen , oxygen and some other gases behaves like ideal gas.

### Ideal gas equation:

Pv = nR’T

Here ,

P = Presure

V= Volume

N = Number of moles

R’ =Universal gas constant

= 8.314 KJ/ K-mol.Kelvin

T = Temperature

It can also write like :

Pv=mrt

Where ,

M = mass ( in Kg)

R = Characteristic Gas constant (KJ/Kg -Kelvin )

### Relationship between R’ and R :

R = R’/ (MOLECULAR weight)

R’ stands for Universal gas constant whose value remains fixed always and it is 8.314 KJ/ K-mol.Kelvin

Whereas,

R stands for characteristic gas constant and it’s value is different for different gas.

#### For example :

##### For air –

Molecular weight = 29 g/mol = 29 × 10-3 Kg/mol

We know that , R = R’/Molecular weight

Rair = 8.314 / 29 = 0.287

Rair = 0.287 KJ/ Kg – Kelvin

Similarly ,

Rwater vapour = 0.416 KJ/ Kg -Kelvin