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Bolye's Law

Robert Boyle, in 1662, recorded the first set of observations between pressure and volume of air. His observations, given below, were also found to be applicable to other gases. At constant temperature, the volume of a definite mass of a gas is inversely proportional to its pressure. Mathematically, we write it as
V α 1 / p
orV = K/p or pV = K      (5.1)

Where K is constant of proportionality. Its value depends upon the mass and temperature of the gas.
According to eq. (5.1), the product of pressure and volume of a given mass of a gas remains constant provided its temperature is held constant. Such behavior is shown in Fig.
Equation (5.1) can also be represented graphically by plotting p versus V as shown in Fig. The nature of the curve is a rectangular hyperbola. The general term isotherm or isothermal (meaning at constant temperature) is used to describe these curves. Alternatively, if p is plotted against 1/V, one would get a straight line as shown in Fig. 
For a given mass of a gas at constant temperature, Boyle's law gives
p1V1 = p2V2                                   (5.2)
Where V1 and V2 are the volumes of the gas at pressures p1 and p2, respectively.
Problem 3.1
A weather balloon has a volume of 175 dm3 when filled with hydrogen at pressure of 1 atm. Calculate its volume at the height of 2 km where the atmospheric pressure is 0.8 atm. Assume that the temperature is constant.

We have
p1  = 1 atm           p2 =0.8 atm
V1 = 175 dm3        V2 = ?
Making use of Boyle's law (p2V2 = P1V1), we get
     = 218.75 dm3m

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