A scuba diver takes a 2.3 balloon from the surface, where the pressure is 1.1 and the temperature is 28, to a depth of 35 , where the pressure is 4.5 and the temperature is 14.
no units
To calculate the change in volume of the balloon as it is taken from the surface to a depth of 35 meters, we can use the ideal gas law equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Let's first convert the temperatures to Kelvin by adding 273.15 to each temperature value.
Surface temperature = 28 + 273.15 = 301.15 K
Depth temperature = 14 + 273.15 = 287.15 K
The ideal gas law equation can be rearranged as:
V1 / T1 = V2 / T2
where V1 is the initial volume at the surface, T1 is the initial temperature at the surface, V2 is the final volume at a depth of 35 meters, and T2 is the final temperature at a depth of 35 meters.
We are given the following values:
P1 (surface pressure) = 1.1 atm
T1 (surface temperature) = 301.15 K
P2 (depth pressure) = 4.5 atm
T2 (depth temperature) = 287.15 K
Let's substitute these values into the equation:
V1 / 301.15 = V2 / 287.15
To solve for V2, we need to isolate it on one side of the equation. Multiply both sides by 287.15:
V1 = V2 * (301.15 / 287.15)
Divide both sides by (301.15 / 287.15):
V1 / (301.15 / 287.15) = V2
Simplify the right side of the equation:
V1 / 1.050946 = V2
Now, substitute the value of V1, which is 2.3 liters, into the equation:
2.3 / 1.050946 = V2
Calculating this equation gives us:
V2 ≈ 2.187 liters
Therefore, the volume of the balloon at a depth of 35 meters is approximately 2.187 liters.