At a pressure of 10$^5$Nm$^{-2}$, a gas has a volume of 20m$^3$. Calculate the volume at 4 x 10$^5$Nm$^{-2}$ at constant temperature.

Analyze the question: The temperature is constant and the pressure changes, so we need Boyle's Law.

Concept: Boyle's Law says that for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume:

P₁V₁ = P₂V₂

Solution:

Given:

• P₁ = 10⁵ N/m²
• V₁ = 20 m³
• P₂ = 4 × 10⁵ N/m²
• V₂ = ?

V₂ = (P₁V₁) / P₂

V₂ = (10⁵ × 20) / (4 × 10⁵)

V₂ = 20 / 4

V₂ = 5 m³

It also makes sense physically: the pressure became 4 times larger, so the volume must shrink to one quarter of its original size (20 ÷ 4 = 5).

Answer: D (5 m³)

Exam tip: At constant temperature, if the pressure is multiplied by a number, divide the volume by the same number. Notice that the 10⁵ cancels, so you don't need to work with large powers of ten. Just compare the ratio 1 : 4.