### Boyle’s law

##
**Boyle’s law**

On the basis
of his experiments, Robert Boyle reached to the conclusion that at constant
temperature, the pressure of a fixed amount (i.e. number of moles n) of gas
varies inversely with its volume. This is known as Boyle’s law. Mathematically,
it can be written as

Where k

_{1}is the proportionality constant. The value of constant k_{1}depends upon the amount of the gas, temperature of the gas and the units in which p and v are expressed.
On
rearranging equation we obtained

*p*V= k_{1}

_{}
It means hat
at constant temperature, product of pressure and volume of a fixed amount of
gas is constant.

If a fixed
amount of gas at constant temperature T occupying volume V

_{1}at pressure*p*_{1}undergoes expansion, so that volume becomes V_{2}and pressure becomes*p*_{2}, then according to Boyle’s law:
The above
figure two conventional ways of graphically presenting Boyle’s law. Fig.5.5(a)
is the graph of equation at different temperatures. The value of k

_{1}for each curve is different because for a given mass of gas, it varies only with temperature. Each curve corresponds to a different constant temperature and is known as an**isothern**(constant temperature plot). Higher curves correspond to higher temperature. It should be noted that volume of the gas doubles if pressure is halved. Table 5.1 gives effect of pressure on volume of 0.09 mol of CO_{2}at 300k.
Fig 5.5 (b) represents
the graph between p and 1/V. it is a straight line passing through origin. However
at high pressures, gases deviate from Boyle’s law and under such conditions a straight
line is not obtained in the graph.

Experiments of
Boyle, in a quantitative manner prove that gases are highly compressible because
when a given mass of a gas is compressed, the same numbers of molecules occupy a
smaller space. This means that gases become denser at high pressure. A relationship
can be obtained between density and pressure of a gas by using Boyle’s law:

This shows
that at a constant temperature, pressure is directly proportional of the
density of a fixed mass of the gas.

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