07 3.2 Boyle's law
Boyle's law: At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.
V ∝ 1/P → P V = constant (fixed mass, constant temperature)
or for two states: P₁V₁ = P₂V₂.
The graph of P against V (constant T) is a curve (a hyperbola); the graph of V against 1/P is a straight line through the origin; the graph of PV against P is a horizontal line.
Example 1. A gas occupies 600 cm³ at 76 cm Hg. It is compressed at constant temperature to 400 cm³. P₂ = P₁V₁/V₂ = 76 × 600/400 = 114 cm Hg.
Example 2. The pressure of a gas is tripled at constant temperature. Its volume becomes one-third.
Example 3. 8 cm³ of air is at the bottom of a lake at a depth where the total pressure is 3 atm. The temperature is the same at the surface. At the surface (1 atm): V = 3 × 8 = 24 cm³.
Example 4 (barometer-tube). A tube holds 40 cm³ of air at atmospheric pressure of 76 cm Hg. The air is pushed to 25 cm³ by raising the movable tube. P = 76 × 40/25 = 121.6 cm Hg, so h = 121.6 − 76 = 45.6 cm Hg.