1. A 3.0 gallon can, open to the surroundings, is sealed when the pressure is 1.0 atmospheres. The can is crushed to a volume of 1.5 gallon. What is the new pressure of air inside the can?
2. The can from question 1 is crushed even further until the pressure in the can is 5.0 atmospheres. What is the internal volume of the can now?
assuming constant temperature, just plug in your numbers and solve for P2 in
P1*V1 = P2*V2
How do I convert 3 gallon can to volume
3 gallons IS a volume
Since you are using the same volume units on both sides of the equation, the actual units do not matter. There is no need to convert gallons to in^3 or cm^3 or liters.
So, for the 1st one, 1/2 the volume means twice the pressure.
To solve both questions, we will use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional, assuming the temperature remains constant.
1. Answer to question 1:
To find the new pressure inside the can after it is crushed to a volume of 1.5 gallons, we can use Boyle's Law. Boyle's Law can be represented as P₁V₁ = P₂V₂, where P₁ is the initial pressure, V₁ is the initial volume, P₂ is the new pressure, and V₂ is the new volume.
Given:
P₁ = 1.0 atmospheres
V₁ = 3.0 gallons
V₂ = 1.5 gallons
Let's plug in these values into the equation and solve for P₂:
P₁V₁ = P₂V₂
(1.0 atm)(3.0 gal) = P₂(1.5 gal)
3.0 atm-gal = 1.5P₂
To isolate P₂, we divide both sides of the equation by 1.5:
(3.0 atm-gal) / 1.5 gal = P₂
2.0 atm = P₂
Therefore, the new pressure inside the can after it is crushed to 1.5 gallons is 2.0 atmospheres.
2. Answer to question 2:
To find the internal volume of the can after further crushing until the pressure inside is 5.0 atmospheres, we can use Boyle's Law again.
Given:
P₁ = 1.0 atmospheres
V₁ = 3.0 gallons
P₂ = 5.0 atmospheres
Let's plug in these values into the equation and solve for the new volume:
P₁V₁ = P₂V₂
(1.0 atm)(3.0 gal) = (5.0 atm)(V₂)
3.0 atm-gal = 5.0V₂
To isolate V₂, we divide both sides of the equation by 5.0:
(3.0 atm-gal) / 5.0 atm = V₂
0.6 gal = V₂
Therefore, the internal volume of the can after further crushing until the pressure inside is 5.0 atmospheres is 0.6 gallons.