What will be the minimum pressure required to compress 500 dm³ of air at 1 bar to 200 dm³, if temperature is kept constant?

Given,

V₁ = Initial volume of the gas = 500 dm³
P₁ = Initial pressure of the gas = 1 bar.
V₂ = Final volume = 200 dm³
P₂ = Final pressure of the gas = ?

By Boyle's Law:

$\text{P}$1 \text{V}1 = \text{P}2 \text{V}2

Substituting the values :

$1 \times 500 = \text{P}$2 \times 200 \\[0.5em] \text{P}2 = \dfrac{500}{200} \\[0.5em] \text{P}_2 = 2.5 \text{ bar }

∴ Final pressure of the gas = 2.5 bar.