Boyle's law

Remarks

It is the special case $T$ and $n$ fixed of the ideal gas law $pV = nRT$. The states of an isothermal process of an ideal gas therefore lie on a hyperbola in the $(V, p)$ plane. Example: if air in a syringe at $100\,\mathrm{kPa}$ is slowly compressed from $30\,\mathrm{ml}$ to $10\,\mathrm{ml}$ at constant temperature, its pressure becomes $300\,\mathrm{kPa}$. Both hypotheses matter. If the compression is fast, the gas warms and the pressure rises faster than $1/V$. For a real gas at high pressure, $pV$ varies at fixed temperature, as the virial expansion shows.

Going deeper

For a student

Boyle's law was one of the first quantitative laws of gases, found from experiments in the seventeenth century. Together with Charles's law and Avogadro's law it gives the ideal gas law. It is used to compute the work $W = nRT \ln(V_2/V_1)$ done by an ideal gas in a reversible isothermal expansion, obtained by integrating $p = nRT/V$.