Verification of (Boyle’s + Charles) Law



VERIFY BOYLE’S LAW WITH THE HELP OF K.M.T
According to Boyle’s law at constant temperature, pressure & volume of a gas are related as:
PV = constant
According to Kinetic theory, pressure of a gas is
P = (1/3) r Since [mN/V = r ]
PV = (1/3) mN 
Multiplying and dividing by 2 on R.H.S
PV = (2/3) N (1/2 m)since (1/2 m) = (K.E)av
therefore

PV = (2/3) N (K.E)av
We know that K.E. is proportional to temperature. Since temperature is constant therefore K.E. will also be constant and 2N/3 is also a constant factor. Thus the factor 2/3 N (K.E)av is constant.
PV = constant
Which is according to Boyle’s law.

VERIFY CHARLES LAW WITH THE HELP OF K.M.T
According to Charles law at constant pressure, absolute temperature & volume of a gas are related as:
V/T = constant
According to Kinetic theory, pressure of a gas is
P =( 1/3) r 
Since [mN/V = r ]
P = (1/3) mN/V 
Multiply and dividing by 2 on R.H.S
P =( 2/3) (N/V) (1/2m)
Since [1/2 m = (K.E)av]
V = (2N/3P) (1/2 m)
V = (2N/3P) (K.E.)av
Since K.E. is proportional to temperature therefore we can replace (K.E.)av by T.
Therefore
V = (2N/3P) T
As (2N/3P) is a constant factor,Therefore,
V = (constant) T
V/T = constant
Which is according to Charles law.