A quantity of gas in a piston cylinder has a volume of 0.544 m3 and a pressure of 200 Pa. The piston compresses the gas to 0.126 m3 in an isothermal (constant-temperature) process. What is the final pressure of the gas?
??__Pa
p1•V1=p2•V2
p2=p1•V1/V2
yes
To find the final pressure of the gas, we can use the ideal gas law, which states:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
Since the process is isothermal (constant temperature), we can assume that T remains constant throughout.
In this question, we are not given the number of moles of gas or the temperature, but since we are only interested in the final pressure, we can use the initial pressure and volume to find the final pressure.
First, we divide the initial volume by the final volume:
V1/V2 = (P2/P1)
Where V1 is the initial volume, V2 is the final volume, P1 is the initial pressure, and P2 is the final pressure.
Plugging in the given values:
0.544 / 0.126 = P2 / 200
Now, we solve for P2:
P2 = (0.544 / 0.126) * 200
P2 ≈ 863.49 Pa
Therefore, the final pressure of the gas is approximately 863.49 Pa.
To determine the final pressure of the gas, we can use the Boyle's Law equation, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.
Boyle's Law equation:
P1V1 = P2V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
From the given information, we know:
P1 = 200 Pa
V1 = 0.544 m3
V2 = 0.126 m3
Substituting the values into the equation:
200 Pa * 0.544 m3 = P2 * 0.126 m3
To find P2, isolate P2 on one side of the equation:
P2 = (200 Pa * 0.544 m3) / 0.126 m3
Now we can calculate the final pressure:
P2 = 872 Pa
Therefore, the final pressure of the gas is 872 Pa.