According to Boyle's law, the volume V of a gas at a constant temperature varies inversely with the pressure P. When the volume of a certain gas is 125 cubic meters, the pressure is 20 psi (pounds per square inch).
If the volume of gas is increased to 400 cubic meters, the pressure will be
At constant temperature (which is what they want you to assume),
P*V = constant
125*20 = 400*P2
P2 = final pressure = (125/400)*20
= 6.25 psi
Since the equation
P1/P2 = V2/V1
involves dimensionless ratios, I did NOT have to convert pressure from psi to Pascal units and back again. I chose to keep pressure in psi and volume in cubic meters
To find the pressure when the volume is increased to 400 cubic meters, we can use Boyle's law. Boyle's law states that the volume of a gas at a constant temperature is inversely proportional to the pressure.
Mathematically, this can be represented as:
V1 * P1 = V2 * P2
where V1 and P1 are the initial volume and pressure, V2 is the final volume (400 cubic meters), and P2 is the final pressure.
Given that the initial volume (V1) is 125 cubic meters and the initial pressure (P1) is 20 psi, we can substitute these values into the equation:
V1 * P1 = V2 * P2
125 * 20 = 400 * P2
Now, we can solve for P2:
P2 = (125 * 20) / 400
P2 = 6250 / 400
P2 = 15.625 psi
Therefore, when the volume of gas is increased to 400 cubic meters, the pressure will be approximately 15.625 psi.