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.
answered @ 7:10 PM
To solve this problem, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume at a constant temperature.
Boyle's Law formula is: P1 * V1 = P2 * V2
Where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
Initial volume (V1) = 10.0 L
Initial pressure (P1) = 200 kPa
Final volume (V2) = 3.10 L
Let's plug these values into Boyle's Law formula and solve for P2:
P1 * V1 = P2 * V2
(200 kPa) * (10.0 L) = P2 * (3.10 L)
2000 = 3.10 * P2
To find P2, divide both sides of the equation by 3.10:
(2000) / (3.10) = P2
P2 ≈ 645.161 kPa
Rounding this to three significant digits, the final pressure of the gas is approximately 645 kPa.
To calculate the final pressure of the gas, we can use Boyle's Law, which states that the pressure and volume of a given amount of gas are inversely proportional when the temperature and the amount of gas remain constant.
Boyle's Law equation is represented as follows: P₁V₁ = P₂V₂
Where:
P₁ and V₁ are the initial pressure and volume of the gas respectively.
P₂ and V₂ are the final pressure and volume of the gas respectively.
In this case:
P₁ = 200. kPa (initial pressure)
V₁ = 10.0 L (initial volume)
V₂ = 3.10 L (final volume)
Now, let's substitute the given values into the equation and solve for P₂:
200. kPa * 10.0 L = P₂ * 3.10 L
Simplifying this equation, we get:
2000 kPa⋅L = 3.10P₂
Next, divide both sides by 3.10 L to isolate P₂:
2000 kPa⋅L / 3.10 L = P₂
Finally, evaluate the expression on the left side to calculate the final pressure:
P₂ ≈ 645.16 kPa
So, the final pressure of the gas is approximately 645.16 kPa, rounded to three significant digits.