A container of gas at 53 psi is compressed to
one third its original volume. What is the
new pressure of the gas?
To find the new pressure of the gas after it is compressed to one third its original volume, we need to use the principle known as Boyle's Law. Boyle's Law states that the pressure and volume of a gas are inversely proportional when the temperature is constant.
To solve this problem, we can set up the relationship using Boyle's Law formula:
P1 * V1 = P2 * V2
Where:
P1 = original pressure of the gas (53 psi)
V1 = original volume of the gas
P2 = new pressure of the gas (unknown)
V2 = new volume of the gas (one third of the original volume)
Since the original volume is not given in the problem, we can assume it to be any value, let's take it as 'V0' for simplicity.
Substituting these values into the equation, we get:
53 psi * V0 = P2 * (1/3) * V0
Now, we can simplify the equation and solve for P2:
53 psi * V0 = (P2 * V0) / 3
Multiply both sides of the equation by 3 and divide by V0:
3 * 53 psi = P2
Now, we can calculate the new pressure of the gas:
P2 = 159 psi
Therefore, the new pressure of the gas after compression is 159 psi.
To find the new pressure of the gas after it is compressed to one-third of its original volume, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional, assuming the temperature remains constant.
Boyle's Law formula is:
P₁V₁ = P₂V₂
Where:
P₁ = Initial pressure
V₁ = Initial volume
P₂ = Final pressure
V₂ = Final volume
In this case, we know that the initial pressure (P₁) is 53 psi, and the initial volume (V₁) is the original volume. Let's call the original volume V₀. The final volume (V₂) is one-third of V₀.
So, the equation becomes:
53 psi * V₀ = P₂ * (1/3) * V₀
Simplifying the equation, we can cancel out the V₀ terms:
53 psi = (1/3) P₂
Solving for P₂, we can multiply both sides of the equation by 3:
53 psi * 3 = P₂
Now, let's calculate the value:
P₂ = 159 psi
Therefore, the new pressure of the gas after it is compressed to one-third of its original volume is 159 psi.