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 volume and pressure is equal to the product of the final volume and pressure. Mathematically, this can be written as:
V1 * P1 = V2 * P2
Where
V1 = initial volume = 0.08 cubic meter
P1 = initial pressure = 1.5 x 10^6 Pascals
V2 = final volume (to be determined)
P2 = final pressure = 4 x 10^6 Pascals
Substituting the given values into the equation, we can solve for V2:
0.08 * 1.5 x 10^6 = V2 * 4 x 10^6
Rearranging the equation to solve for V2:
V2 = (0.08 * 1.5 x 10^6) / (4 x 10^6)
V2 = (0.12 x 10^6) / (4 x 10^6)
V2 = 0.03
Therefore, when the pressure is changed to 4 x 10^6 Pascals, the volume of the gas will be 0.03 cubic meters.