Deduce (a) Boyle's law and (b) Charles law from Kinetic gas equation.

Explanation

(a) Boyle.s law : According to kinetic theory the averge K.E of gas molecules is directly proportional to the absolute temperature.
(i.e.) `KE prop "T. But K.E" = (1)/(2) mnc^(2)`
`therefore (1)/(2) mnc^(2) prop T (or) (1)/(2) mnc^(2) = KT`
According to kinetic gas equation, `PV = (1)/(3) mnc^(2)`
(or) `PV = (2)/(3) xx (1)/(2) mnc^(2) (or) PV = (2)/(3) xx KT (or) V = (2)/(3) (K)/(P) T`
If .T. is kept constant, then V = Constant `xx (1)/(P) (or) V prop (1)/(P)` (T constant)
At constant temperature, the volume of a given mass of gas is inversely proportional to its pressure. This is Boyle.s law.
(b) Charles. law : According to kinetic theory, the average K.E of gas molecules is directly proportional to the absolute temperature.
(i.e.) `K.E prop "T. But K.E" = (1)/(2) mnc^(2)`
`therefore (1)/(2) mnc^(2) prop T (or) (1)/(2) mnc^(2) = KT`
According to kinetic gas equation, `PV = (1)/(3) mnc^(2)`
(or) `PV = (2)/(3) xx (1)/(2) mnc^(2) (or) PV = (2)/(3) xx KT (or) V = (2)/(3) (KT)/(P)`
If .P. is kept constant, then V = constant `xx` T (or) V `prop` T (P constant)
At constant pressure, the volume of a given mass of gas is directly proprtional to its absolute temperature. This is Charles. law.