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.