What is Pressure?

Example 7.2 (Heel versus snowshoe)

A $60\,\mathrm{kg}$ person weighs $F = 60 \times 9.81 \approx 590\,\mathrm{N}$. On one stiletto heel of $1.0\,\mathrm{cm}^{2}$ = $1.0 \times 10^{-4}\,\mathrm{m}^{2}$: $P = 590/1.0 \times 10^{-4} \approx 5.9 \times 10^{6}\,\mathrm{Pa} = 5.9\,\mathrm{MPa}$. On two snowshoes of $0.20\,\mathrm{m}^{2}$ each: $P = 590/0.40 \approx 1.5\,\mathrm{kPa}$. The same weight presses $4000$ times harder under the heel: heels pockmark wooden floors, snowshoes float on powder snow.

Example 20.14 (How incompressible)

Water at the bottom of the Mariana trench ($1100\,\mathrm{bar}$) is compressed by $\chi_T\Delta P \approx 5\times10^{-10} \times 1.1\times10^8 = 5\%$; a $30\,\mathrm{m}$ steel rail warmed by $50$ K lengthens by $\alpha L\Delta T = 18\,\mathrm{mm}$ — the reason for expansion joints. Against a gas, whose volume halves under a doubled pressure, the model of a fixed volume is good to a few percent in most situations of this volume.