A cylinder is filled with 10.0L of gas and a piston is put into it. The initial pressure of the gas is measured to be 200.kPa.
The piston is now pushed down, compressing the gas, until the gas has a final volume of 3.10L. Calculate the final pressure of the gas. Round your answer to 3significant digits.
pressure is inversely proportional to volume ... p v = k
10.0 * 200. = 3.10 * ?
To find the final pressure of the gas, we can use the principles of Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.
According to Boyle's Law, P1V1 = P2V2, where P1 is the initial pressure, V1 is the initial volume, P2 is the final pressure, and V2 is the final volume.
Given:
Initial pressure, P1 = 200. kPa
Initial volume, V1 = 10.0 L
Final volume, V2 = 3.10 L
Using Boyle's Law, we can rearrange the equation to solve for the final pressure, P2:
P2 = (P1 * V1) / V2
Substituting the given values:
P2 = (200. kPa * 10.0 L) / 3.10 L
Calculating the value:
P2 = 645.16 kPa
Therefore, the final pressure of the gas is approximately 645.16 kPa, rounding to three significant digits.
To calculate the final pressure of the gas, we can use the relationship between pressure and volume known as Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is constant. The equation for Boyle's Law is:
P1 * V1 = P2 * V2
Where P1 and V1 represent the initial pressure and volume, and P2 and V2 represent the final pressure and volume, respectively.
Given:
P1 = 200 kPa
V1 = 10.0 L
V2 = 3.10 L
We can rearrange the equation to solve for P2:
P2 = (P1 * V1) / V2
Substituting the given values:
P2 = (200 kPa * 10.0 L) / 3.10 L
P2 = 2000 kPa / 3.10 L
P2 ≈ 645.161 kPa
Therefore, the final pressure of the gas is approximately 645.161 kPa (rounded to 3 significant digits).