Boyle's Law (Pressure - Volume Relationship)

The law: pressure and volume vary inversely

From his experiments, Robert Boyle concluded that at constant temperature, the pressure of a fixed amount (fixed number of moles, $n$) of gas varies inversely with its volume. This is Boyle's Law. Mathematically:

Here $k_1$ is a proportionality constant whose value depends on the amount of gas, its temperature, and the units chosen for $p$ and $V$. Rearranging gives the more familiar form:

In words: at constant temperature, the product of pressure and volume of a fixed amount of gas stays constant. If a fixed amount of gas at temperature $T$ moves from ($p_1$, $V_1$) to ($p_2$, $V_2$):

Reading the graphs

Figure 5.5 shows Boyle's law two conventional ways. Fig. 5.5(a) plots $p$ against $V$ directly: each curve is a rectangular-hyperbola-shaped isotherm (a constant-temperature curve), with a different $k_1$ for each temperature — higher curves correspond to higher temperature. Notice that volume doubles whenever pressure is halved. Fig. 5.5(b) instead plots $p$ against $1/V$, which turns the relationship into a straight line through the origin — though at very high pressures, real gases start to deviate and the line bends away from straight.

Table 5.1 shows this constancy of $pV$ numerically, for 0.09 mol of CO$_2$ at 300 K:

$pV$ stays close to $22.4\times10^2$ throughout, confirming Boyle's law.

Compressibility and density …