*Boyle' Law :** The volume of a given mass of gas is inversely proportional to its pressure at constant temperature.
V α 1/p at constant temperature
*Charle' Law :** a) The volume of a given mass of gas is directly proportional to its absolute temperature, pressure remaining constant. i.e., V α T
(b) The pressure of a given mass of gas is directly proportional to its absolute temperature, volume remaining constant. i.e., P α T at constant volume.
Ideal gas equation : Consider a given mass of gas having a volume V1 at a pressure P1 and absolute temperature T1. When the temperature is changed to T2. Let the gas occupy a volume V2 at a pressure P2.
Let this change take place in two steps.
(i) Keeping the temperature constant at T1K. Let the pressure of the gas be changed from P1 to P2. The volume of gas changes from V1 to V(say).
From Boyle'* law, P1V1 = P2V; V = P1V1/P2 –––– (1)
(ii) Now keeping the pressure of the gas constant at P2. Let the temperature be changed from T1 to T2. Then the volume of the gas changes from V1 to V2.
Applying Charles law, V/T1 = V2/T2; V = V2T1/T2––––– (2)
From equations (1) and (2) P1V1/P2 = V2T1/T2
P1V1/T1 = P2V2/T2; PV/T = r
This constant depends on the mass and nature of the gas. This constant for one gram of gas at STP is called its gas constant and changes from gas to gas. But then 1 gram mole of the gas is considered this comes out to be a universal gas constant R. Then the gas equation can be written as PV = RT.
From Boyle'* law and Charles law, Charles law is better for the purpose of thermometry with increasing temperature, pressure and volume of the gas also increases. At constant pressure, volume is proportional to absolute temperature. And at constant volume, pressure is proportional to absolute temperature.
