Boyle's Law #

This section defines Boyle's Law which states that absolute pressure of an ideal gas is inversely proportional to the volume it occupies at constant temperature in a closed thermodynamic system.
$$ P ∝ \frac{1}{V} $$ or $$ P V = k $$

where:

P is pressure
V is volume
k is a constant for a given sample of gas and depends only on the mass of the gas and the temperature

Assumption #

The model assumes:

ideal gas law for state 1 and state 2 (PV = nRT)
equal temperature (T1 = T2)
equal number of moles (n1 = n2)

A better proof for Boyle's law, following from the properties of a thermodynamic system, is shown here. #

source

theorem Boyle (P1 P2 V1 V2 T1 T2 n1 n2 R : ℝ) (a1 : P1 * V1 = n1 * R * T1) (a2 : P2 * V2 = n2 * R * T2) (a3 : T1 = T2) (a4 : n1 = n2) :

P1 * V1 = P2 * V2