the gas contained in a piston is compressed from an original volume of 1.15 L to a new volume of 0.45 L. Assuming that the temperature of the gas remains constant what is the new pressure exerted on the gas if the original pressure was 2.15 atm?
To find the new pressure exerted on the gas, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.
Boyle's Law can be written as:
P₁ * V₁ = P₂ * V₂
Where:
P₁ = initial pressure
V₁ = initial volume
P₂ = final pressure (unknown)
V₂ = final volume
Given:
P₁ = 2.15 atm (initial pressure)
V₁ = 1.15 L (initial volume)
V₂ = 0.45 L (final volume)
Let's substitute the given values into the equation:
2.15 atm * 1.15 L = P₂ * 0.45 L
Now we can solve for P₂:
2.15 * 1.15 = P₂ * 0.45
2.4725 = P₂ * 0.45
Divide both sides of the equation by 0.45:
2.4725 / 0.45 = P₂
P₂ ≈ 5.49 atm
Therefore, the new pressure exerted on the gas is approximately 5.49 atm.