Question
Give its
(i) mathematical expression
(ii) graphical representation and
(iii) significance.
(i) mathematical expression
(ii) graphical representation and
(iii) significance.
✓
Answer
(i) mathematical expressionsuppose a gas occupies volume $\mathrm{V}_1$ when its pressure is $\mathrm{P} 1$; then
$\begin{aligned} & \mathrm{V}_1 \propto \frac{1}{\mathrm{P}_1} \text { or }
\mathrm{V}_1=\frac{\mathrm{k}}{\mathrm{P}_1} \\ & \mathrm{P}_1
\mathrm{~V}_1=\mathrm{k}=\mathrm{constant}\end{aligned}$
If $V_2$ is the volume ocuupied when the pressure is $P_2$ at the same temperature, the
$ \begin{aligned}& \mathrm{V}_2 \propto \frac{1}{\mathrm{P}_2} \text { or } \mathrm{V}_2=\frac{\mathrm{k}}{\mathrm{P}_2} \\& \mathrm{P}_2 \mathrm{~V}_2=\mathrm{k}=\mathrm{constant}\end{aligned}$
$\mathrm{P}_1\mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2=\mathrm{k}$ at constant temperature
This is called Boyle's law equation.
(ii) graphical representation
The law canbe verified by plotting a graph
(a) $\vee$ vs $\frac{1}{p}$(b) V vs P(c) PV vs P
(a) (\mathrm{V}$ vs $\frac{1}{p}$ : 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 gasbecomes denser. Thus at a constant temperature, the density of a gas is directly proportional toits pressure.
Atmospheric pressure is low at high altitudes, so air is less dense. Hence, alesser quantity of oxygen is available for breathing. This is the reason why mountaineers have to carryoxygen cylinders with them.
$\begin{aligned} & \mathrm{V}_1 \propto \frac{1}{\mathrm{P}_1} \text { or }
\mathrm{V}_1=\frac{\mathrm{k}}{\mathrm{P}_1} \\ & \mathrm{P}_1
\mathrm{~V}_1=\mathrm{k}=\mathrm{constant}\end{aligned}$
If $V_2$ is the volume ocuupied when the pressure is $P_2$ at the same temperature, the
$ \begin{aligned}& \mathrm{V}_2 \propto \frac{1}{\mathrm{P}_2} \text { or } \mathrm{V}_2=\frac{\mathrm{k}}{\mathrm{P}_2} \\& \mathrm{P}_2 \mathrm{~V}_2=\mathrm{k}=\mathrm{constant}\end{aligned}$
$\mathrm{P}_1\mathrm{~V}_1=\mathrm{P}_2 \mathrm{~V}_2=\mathrm{k}$ at constant temperature
This is called Boyle's law equation.
(ii) graphical representation
The law canbe verified by plotting a graph
(a) $\vee$ vs $\frac{1}{p}$(b) V vs P(c) PV vs P
(a) (\mathrm{V}$ vs $\frac{1}{p}$ : 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 gasbecomes denser. Thus at a constant temperature, the density of a gas is directly proportional toits pressure.
Atmospheric pressure is low at high altitudes, so air is less dense. Hence, alesser quantity of oxygen is available for breathing. This is the reason why mountaineers have to carryoxygen cylinders with them.
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