A balloon filled with 3.5 L of helium at 20 °C and 3 atm. What will be the new pressure if its volume increases to 17.5 L at constant temperature?
PV = kT.
So, PV/T is constant. In fact, since T is constant as well, PV is constant. You want P so that
17.5P = 3*3.5
To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional, assuming that the temperature remains constant. Mathematically, Boyle's Law can be expressed as:
P₁V₁ = P₂V₂
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
Given:
P₁ = 3 atm
V₁ = 3.5 L
V₂ = 17.5 L
T = Constant
Let's substitute these values into the equation and solve for P₂:
P₁V₁ = P₂V₂
3 atm * 3.5 L = P₂ * 17.5 L
10.5 atm-L = 17.5 P₂
Now divide both sides by 17.5 to solve for P₂:
P₂ = (10.5 atm-L) / 17.5
P₂ ≈ 0.6 atm
Therefore, the new pressure of the balloon would be approximately 0.6 atm when its volume increases to 17.5 L at constant temperature.
To find the new pressure of the balloon when its volume increases to 17.5 L at constant temperature, we can use Boyle's Law. Boyle's Law states that the pressure exerted by a gas is inversely proportional to its volume, as long as the temperature remains constant.
Boyle's Law can be mathematically represented as:
P1 × V1 = P2 × V2
where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
Given:
Initial volume of the balloon (V1) = 3.5 L
Initial pressure of the balloon (P1) = 3 atm
Final volume of the balloon (V2) = 17.5 L (after the volume increases)
Final pressure of the balloon (P2) = ?
Plugging in the values into the equation, we get:
3 atm × 3.5 L = P2 × 17.5 L
To solve for P2, divide both sides of the equation by 17.5 L:
(3 atm × 3.5 L) / 17.5 L = P2
Multiply and divide:
10.5 atm L / 17.5 L = P2
Now, simplify:
10.5 atm / 17.5 = P2
Calculating this value, we find:
P2 ≈ 0.6 atm
Therefore, the new pressure of the balloon will be approximately 0.6 atm when its volume increases to 17.5 L at constant temperature.