# JEE Main & Advanced Chemistry States of Matter Boyle's law

## Boyle's law

Category : JEE Main & Advanced

(1) In 1662, Robert Boyle discovered the first of several relationships among gas variables (P, T, V).

(2) It states that, “For a fixed amount of a gas at constant temperature, the gas volume is inversely proportional to the gas pressure.”

Thus, $P\propto 1/V$ at constant temperature and mass

or $P=K/V$ (where K is constant)

or$PV=K$ or ${{P}_{1}}{{V}_{1}}={{P}_{2}}{{V}_{2}}=K$ (For two or more gases)

(3) Graphical representation of Boyle's law : Graph between P and V at constant temperature is called isotherm and is an equilateral (or rectangular) hyperbola. By plotting P versus $1/V$, this hyperbola can be converted to a straight line. Other types of isotherms are also shown below,

(4) At constant mass and temperature density of a gas is directly proportional to its pressure and inversely proportional to its volume.

Thus, $d\propto P\propto \frac{1}{V}$             $\left[ \because V=\frac{\text{mass}}{d} \right]$

or $\frac{{{d}_{1}}}{{{d}_{2}}}=\frac{{{P}_{1}}}{{{P}_{2}}}=\frac{{{V}_{2}}}{{{V}_{1}}}=.......=K$

(5) At altitudes, as P is low d of air is less. That is why mountaineers carry oxygen cylinders.

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