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Question
Give its
(i) mathematical expression
(ii) graphical representation and
(iii) significance.
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Solution
(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.
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