A container of gas at 24 psi is compressed to one eighth its original volume. What is the new pressure of the gas? Answer in units of psi.
To find the new pressure of the gas after it is compressed, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume, assuming constant temperature.
Boyle's Law can be expressed as:
P₁V₁ = P₂V₂
Where:
P₁ and V₁ are the initial pressure and volume of the gas,
P₂ and V₂ are the final pressure and volume of the gas.
In this case, we know the initial pressure (P₁) is 24 psi and the final volume (V₂) is one eighth (1/8) of the initial volume (V₁).
So, let's assign some variables:
P₁ = 24 psi (initial pressure)
V₁ = Initial volume (unknown)
P₂ = New pressure (unknown)
V₂ = (1/8) * V₁ (final volume)
Now, we can plug in these values into Boyle's Law equation:
P₁ * V₁ = P₂ * V₂
Substituting the known values:
(24 psi) * V₁ = P₂ * (1/8) * V₁
First, let's cancel out V₁ by dividing both sides by V₁:
24 psi = P₂ * (1/8)
Next, solve for P₂ by multiplying both sides by 8:
192 psi = P₂
Therefore, the new pressure of the gas after being compressed to one eighth its original volume is 192 psi.