P1 V1 = P2 V2
so
V2 = P1 V1/P2
I am assuming that these are total pressures and no "gage" pressures. If they are gage pressures add 1 atm to both P1 and P2
so
V2 = P1 V1/P2
I am assuming that these are total pressures and no "gage" pressures. If they are gage pressures add 1 atm to both P1 and P2
If the initial volume is 500 ml at a pressure of 1.5 atmospheres and we apply a constant temperature to the gas, we can use Boyle's Law to find the new volume. Boyle's Law states that the product of pressure and volume is constant, as long as the temperature remains constant.
So, if the initial pressure (P1) is 1.5 atmospheres and the initial volume (V1) is 500 ml, and we want to find the new volume (V2) at a pressure (P2) of 5 atmospheres, we can use the formula:
P1 x V1 = P2 x V2
Plugging in the values we have:
1.5 x 500 = 5 x V2
Now, let's do some math to find that new volume:
750 = 5 x V2
V2 = 750 / 5
V2 = 150 ml
So, the new volume of the gas, when submerged to a pressure of 5 atmospheres at constant temperature, would be 150 ml. That's a lot of pressure for such a tiny volume. It's like trying to fit an elephant in a clown car!
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature (constant in this case)
P₂ = final pressure
V₂ = final volume (unknown)
T₂ = final temperature (constant in this case)
Since the temperature remains constant (T₁ = T₂), the equation simplifies to:
(P₁ * V₁) = (P₂ * V₂)
Given:
P₁ = 1.5 atm
V₁ = 500 mL = 0.5 L
P₂ = 5 atm
V₂ = unknown
We can plug in the values into the equation and solve for V₂:
(1.5 atm * 0.5 L) = (5 atm * V₂)
0.75 L = 5 atm * V₂
Now, divide both sides of the equation by 5 atm:
(0.75 L) / 5 atm = V₂
V₂ = 0.15 L
Therefore, the final volume of the gas will be 0.15 liters when it is submerged to a pressure of 5 atmospheres at a constant temperature.
Boyle's Law equation: P1 * V1 = P2 * V2
Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
P2 = final pressure of the gas
V2 = final volume of the gas (what we want to find)
We are given:
P1 = 1.5 atmosphere
V1 = 500 ml
P2 = 5 atmosphere (the new pressure)
Let's plug in the given values into the equation and solve for V2:
P1 * V1 = P2 * V2
(1.5 atmosphere) * (500 ml) = (5 atmosphere) * V2
750 ml = 5 atmosphere * V2
Now, we can solve for V2 by dividing both sides of the equation by 5 atmosphere:
V2 = 750 ml / 5 atmosphere
V2 = 150 ml
Therefore, the volume of the gas will be 150 ml when it is submerged to a pressure of 5 atmosphere at constant temperature.