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.
Answers
GPT 3.5
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.
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.