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.

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