Question

Boyle’s law states that at constant temperature, the volume V of a fixed mass of gas is inversely proportional to its absolute pressure P. If a gas occupies a volume of 0.08 cubic meter at a pressure of 1.5 x 10^6 (1,500,000) Pascals, determine the volume (V) if the pressure is changed to 4×10^6 (4,000,000) Pascals.

Answer 1

According to Boyle's law, the product of the initial pressure (P1) and the initial volume (V1) is equal to the product of the final pressure (P2) and the final volume (V2).

P1 * V1 = P2 * V2

We are given:
Initial volume (V1) = 0.08 cubic meters
Initial pressure (P1) = 1.5 x 10^6 Pascals

Final pressure (P2) = 4 x 10^6 Pascals

Let's solve for the final volume (V2):

P1 * V1 = P2 * V2

(1.5 x 10^6) * (0.08) = (4 x 10^6) * V2

1.2 x 10^5 = 4 x 10^6 * V2

V2 = (1.2 x 10^5) / (4 x 10^6)

V2 ≈ 0.03 cubic meters

Therefore, the volume (V) when the pressure is changed to 4 x 10^6 Pascals is approximately 0.03 cubic meters.