**Combined Gas Equation**

The equation which shows simultaneous effect of change of pressure and temperature on volume is called combined gas equation. It is obtained by combining Boyle’s law and Charle’s law.

Accoring to Boyle’s law, at constant temperature volume of certain mass of gas is inversely proportional to pressure.

Mathematically,

V is directly proportional to 1/P ----------(i)

According to Charles law, at constant pressure, volume of certain mass of gas is directly proportional to temperature in Kelvin scale.

mathematically,

V is directly proportional to T -----------(ii)

combining equation (i) and (ii)

V is proportional to T/P

V= KT/P [ where K is proportionality constant]

PV = KT ------------(iii)

K is proportionality constant

For one mole of gas, K constant is universal gas constant or molar gas constant which is represented by ‘R’

Then, PV=nRT -------------(iv)

For ‘n’ mole of gas’

PV=nRT -------------(v)

Equation v is known as ideal gas equation.

Again, from (iii)

PV/T = K -----------(vi)

If pressure ’P

_{1}’ and volume ‘V_{1}’ of gas at temperature ‘T_{1}’ is changed to pressure ‘P_{2}’, volume ‘V_{2}’ and temperature ‘T_{2}’. Then, P

_{1}V_{1}= K ---------------(vii) P

_{2}V_{2}= K ---------------(viii)Combining equation (vii) and (viii)

P

_{1}V_{1}= P_{2}V_{2}-----------------(ix)Equation (ix) is known as the combined gas equation.

## Share on Social Media