Question

Give its

(i) mathematical expression

(ii) graphical representation and

(iii) significance.

Answer 1

(i) mathematical expression

suppose a gas occupies volume V₁ when its pressure is P1; then

`"V"_1 ∝ 1/"P"_1  "or"  "V"_1 = "k"/"P"_1`

`"P"_1"V"_1 = "k" = "constant"`

If V₂ is the volume ocuupied when the pressure is P₂ at the same temperature, the

`"V"_2 ∝ 1/"P"_2  "or"  "V"_2 = "k"/"P"_2`

`"P"_2"V"_2 = "k" = "constant"`

`"P"_1"V"_1 = "P"_2"V"_2 = "k"` at constant temperature.

This is called Boyle's law equation.

(ii) graphical representation

The law can be verified by plotting a graph 
(a) V vs `1/p`   (b) V vs P   (c) PV vs P

(a) V vs `1/p`: a straight line passing through the origin is obtained

(b) V vs P: a hyperbolic curve in the first quadrant is obtained 

(c) PV vs P: a straight line is obtained parallel to the pressure axis.

(iii) Significance 

On increasing pressure, volume decreases. The gas becomes denser. Thus at a constant temperature, the density of a gas is directly proportional to its pressure.

Atmospheric pressure is low at high altitudes, so air is less dense. Hence, a lesser quantity of oxygen is available for breathing. This is the reason why mountaineers have to carry oxygen cylinders with them.