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

Explanation

Deduction of Boyle.s law:
Kinetic gas equation is `PV =1/3 m n u^2`
` PV = 1/3 m n u^2`
` =1/3 xx 2/2 m n u^2`
`=2/3 xx 1/2 m n u^2`
` PV = 2/3 `[ kinetic energy (KE) ] ` [ :. KE_((" .n. moles "))= 1/2 m n u^2]`
`PV =(2)/(3) KT ` [ ` :.` KE = KT according to kinetic theory ]
`PV =(2)/(3) KT `
According to Boyle.s law T is constant
` therefore PV = 2/3 ` ( constant)
` therefore ` PV = constant
` (or )`
` P prop (1 )/(V )`
hence boyle.s law proved kinetic gas equation
B) Deduction of charle.s law :
kinetic gas equation is ` PV = 1/3 m n u^2`
`PV =1/3 m n u^2`
` = 2/2 xx 1/3 m n u^2`
` =2/2 xx 1/2 m n u^2 `
` =2/3 (KE ) ` [ kinetic energy `(KE) =1/2 m n u^2]`
`PV = 2/3 KT ` [ According to kinetic theory KE =KT ]
`(V)/(T ) =2/3 xx (K )/( P)`
Acoording to charle.s law .P. is constant
` therefore (V )/(T ) =` constant (or) ` V prop T `
hence charle.s law proved from kinetic gas equation .