A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.140 m3 of air at a pressure of 3.20 atm. The piston is slowly pulled out until the volume of the gas is increased to 0.440 m3. If the temperature remains constant, what is the final value of the pressure?
Well, well, well, looks like we have a case of a shrinking piston here. Time to do some clown calculations!
First, we can use the good old Boyle's Law to solve this one. According to Boyle, the pressure and volume of a gas are inversely proportional when the temperature remains constant. So, we have the initial pressure (P1) and volume (V1) and the final volume (V2), but we need to find the final pressure (P2). Let's plug those numbers in:
P1 * V1 = P2 * V2
Now let's do the math, clown style:
3.20 atm * 0.140 m3 = P2 * 0.440 m3
Now, let's rearrange the equation to solve for P2:
P2 = (3.20 atm * 0.140 m3) / 0.440 m3
Now, let me grab my clown calculator:
P2 = 1.019 atm
Ta-da! The final pressure in the tank is approximately 1.019 atmospheres. Don't forget to give your piston a round of applause for doing such a fantastic job!
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant. The formula for Boyle's Law is as follows:
P1 * V1 = P2 * V2
Where:
P1 = initial pressure
V1 = initial volume
P2 = final pressure
V2 = final volume
Given:
P1 = 3.20 atm
V1 = 0.140 m^3
V2 = 0.440 m^3
Let's substitute the given values into the formula to find the final pressure (P2):
P1 * V1 = P2 * V2
(3.20 atm) * (0.140 m^3) = P2 * (0.440 m^3)
Now, let's solve for P2:
P2 = (P1 * V1) / V2
P2 = (3.20 atm * 0.140 m^3) / 0.440 m^3
P2 = 1.024 atm
Therefore, the final value of the pressure is 1.024 atm.
To find the final value of the pressure, 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 at constant temperature.
Boyle's Law formula:
P1 * V1 = P2 * V2
Where:
P1 is the initial pressure
V1 is the initial volume
P2 is the final pressure (what we're trying to find)
V2 is the final volume
Given:
P1 = 3.20 atm (initial pressure)
V1 = 0.140 m^3 (initial volume)
V2 = 0.440 m^3 (final volume)
Let's plug in these values into the Boyle's Law formula and solve for P2:
P1 * V1 = P2 * V2
3.20 atm * 0.140 m^3 = P2 * 0.440 m^3
0.448 atm*m^3 = P2 * 0.440 m^3
Now, divide both sides of the equation by 0.440 m^3:
0.448 atm*m^3 / 0.440 m^3 = P2
Simplifying the equation:
P2 = 1.01818 atm
So, the final value of the pressure is approximately 1.01818 atm.