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.
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.
To solve this problem, we can use Boyle's law, which states that the volume and pressure of a gas are inversely proportional at constant temperature. Mathematically, Boyle's law can be expressed as:
P₁V₁ = P₂V₂
where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
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
Now, we can plug in the given values into Boyle's law equation:
P₁V₁ = P₂V₂
(1.5 x 10^6)(0.08) = (4 x 10^6)(V₂)
120,000 = 4V₂
Divide both sides of the equation by 4:
30,000 = V₂
Therefore, the final volume V₂ is 30,000 cubic meters.