A scuba diver takes a 2.3L balloon from the surface, where the pressure is 1.0atm and the temperature is 37degrees C, to a depth of 35m, where the pressure is 4.5atm and the temperature is 18degrees C.what is the final volume at this depth?
(P1V1/T1) = (P2V2/T2)
T must be in kelvin.
8898009
To solve this problem, we can use Boyle's Law, which states that the product of pressure and volume is constant if the temperature remains constant.
Boyle's Law: P1V1 = P2V2
Given:
P1 = 1.0 atm (initial pressure)
V1 = 2.3 L (initial volume)
P2 = 4.5 atm (final pressure)
T1 = 37 degrees C (initial temperature)
T2 = 18 degrees C (final temperature)
First, we need to convert the temperatures from degrees Celsius to Kelvin by adding 273.15:
T1 = 37 + 273.15 = 310.15 K
T2 = 18 + 273.15 = 291.15 K
Now, we can plug the values into Boyle's Law equation and solve for V2:
P1V1 = P2V2
(1.0 atm)(2.3 L) = (4.5 atm)(V2)
Cross-multiplying and solving for V2:
V2 = (1.0 atm)(2.3 L) / (4.5 atm)
V2 = 0.51 L
Therefore, the final volume of the balloon at a depth of 35 m is 0.51 L.
To find the final volume of the balloon at a depth of 35m, where the pressure is 4.5atm and the temperature is 18 degrees Celsius, we can use the combined gas law. The combined gas law formula is:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure
V₁ = initial volume
T₁ = initial temperature
P₂ = final pressure
V₂ = final volume (which we want to find)
T₂ = final temperature
Given:
P₁ = 1.0 atm
V₁ = 2.3 L
T₁ = 37°C (convert to Kelvin by adding 273: 37°C + 273 = 310K)
P₂ = 4.5 atm
T₂ = 18°C (convert to Kelvin: 18°C + 273 = 291K)
Now, substitute these values into the formula and solve for V₂:
(1.0 * 2.3) / (310) = (4.5 * V₂) / (291)
Cross-multiply and solve for V₂:
2.3 * 291 = 4.5 * V₂
669.3 = 4.5 * V₂
Divide both sides by 4.5:
V₂ = 669.3 / 4.5
V₂ = 148.73
Therefore, the final volume of the balloon at a depth of 35m is approximately 148.73 L.