JEE Main & Advanced Chemistry States of Matter / पदार्थ की अवस्थाएँ - गैस एवं द्रव Boyle's Law

(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.