A cylindrical tank has a tight-fitting piston that allows the volume of the tank to change. The tank contains 0.5m^3 of air at a pressure of 2*10^5 Pa. The piston is slowly pushed in until the pressure of the air is increased to 2.5*10^5 Pa. If the temperature remains constant, what is the final value of the volume?
P1V1=P2V2
Solve for V2.
To find the final value of the volume, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
Boyle's Law can be expressed as: P1 * V1 = P2 * V2
Where:
- P1 is the initial pressure
- V1 is the initial volume
- P2 is the final pressure
- V2 is the final volume
In this case, we know the initial pressure (P1 = 2 * 10^5 Pa), the initial volume (V1 = 0.5 m^3), and the final pressure (P2 = 2.5 * 10^5 Pa). We need to find the final volume (V2).
Rearranging Boyle's Law equation to solve for V2 gives us:
V2 = (P1 * V1) / P2
Substituting the values we know:
V2 = (2 * 10^5 Pa * 0.5 m^3) / (2.5 * 10^5 Pa)
V2 = 1 m^3
Therefore, the final value of the volume is 1 m^3.
To find the final volume of the tank, we can use Boyle's Law, which states that the product of the initial pressure and volume is equal to the product of the final pressure and volume, assuming constant temperature.
Boyle's Law equation is expressed as:
P1 * V1 = P2 * V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume, respectively.
Given:
P1 = 2 * 10^5 Pa
P2 = 2.5 * 10^5 Pa
V1 = 0.5 m^3
We can rearrange the equation to solve for V2 (final volume):
V2 = (P1 * V1) / P2
Substituting the given values into the equation:
V2 = (2 * 10^5 Pa * 0.5 m^3) / (2.5 * 10^5 Pa)
V2 = (1 * 10^5 m^3) / (2.5 * 10^5 Pa)
V2 = 0.4 m^3
Therefore, the final value of the volume is 0.4 m^3.