Graphs of Boyle's Law

31st Oct 2019 @ 2 min read

The graph of Boyle's law is known as pressure-volume graph or PV curve. It is as follows:

Boyle's law graph — The curve is called PV curve, and it is hyperbolic in nature.

As observed from the graph above, pressure increases with a decrease in volume, and vice versa. Thus, pressure is inversely proportional to volume. Other parameters (temperature and amount of gas) are constant in the graph above.

Mathematical explanation

Volume is on the x-axis and pressure, on the y-axis. The equation of the curve is PV = k, which is the equation of Boyle's law. The curve is hyperbolic in nature having two asymptotes: P = 0 (horizontal) and V = 0 (vertical).

Note: An asymptote is a line or curve such that the distance between it and a given curve tends to zero as x and/or y coordinates tends to infinity.

As volume tends to positive infinity, pressure tends to zero, and we get the horizontal asymptote, P = 0.

$\lim_{V \to +\infty} P = \lim_{V \to +\infty} \frac{k}{V} = 0$

When volume approaches zero, pressure approaches infinity, and it results in the vertical asymptote, V = 0.

$\lim_{V \to 0^{+}} P = \lim_{V \to 0^{+}} \frac{k}{V} = +\infty$

Graphs at different temperatures

Graphs of Boyle's law can be plotted at different temperatures. Each curve in the graphs below is at a constant temperature and such curves are called isotherms.

Boyle's law graph at differenttemperatures — Pressure vs volume graph at different temperatures

The above graph is a pressure-volume graph plotted at three different temperatures (T₁, T₂, and T₃). As observed from the graph, with an increase in temperature, curves shift upwards. This is because of increase in the value of k.

Boyle's law graph pressure vs inverse volume — The graph of pressure vs inverse volume at different temperatures

The graph of pressure vs inverse volume is a straight line passing through the origin and having the positive slope, k.

Boyle's law pressure volume vs volume graph — The graph of pressure volume vs volume at different temperatures.

The graph above is a straight line parallel to the x-axis. This proves the product of pressure and volume at a constant temperature and amount of gas is constant. The lines in the graph are independent of volume (or pressure).