A scuba diver takes a 2.3 L balloon from the surface, where the pressure is 0.90 atm and the temperature is 28 ∘C, to a depth of 20 m , where the pressure is 3.0 atm and the temperature is 15 ∘C. What is the volume of the balloon at this depth?
P1 * V1 / T1 = P2 * V2 / T2
change ºC to ºK and plug in the values
To find the volume of the balloon at the new depth, we can use Boyle’s Law, which states that the pressure and volume of a gas are inversely proportional when the temperature remains constant.
The equation for Boyle's Law is:
P1V1 = P2V2
Where:
P1 = Initial pressure (0.90 atm)
V1 = Initial volume (2.3 L)
P2 = Final pressure (3.0 atm)
V2 = Final volume (unknown)
We can rearrange the equation to solve for V2:
V2 = (P1V1) / P2
Now we can plug in the given values:
V2 = (0.90 atm * 2.3 L) / 3.0 atm
Calculating this, we get:
V2 = 0.69 L
Therefore, the volume of the balloon at a depth of 20 m would be approximately 0.69 L.
To find the volume of the balloon at a different depth, we can use the combined gas law equation. The combined gas law relates the initial and final pressure, volume, and temperature of a gas sample.
The combined gas law equation is as follows:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (at the surface) = 0.90 atm
V1 = initial volume = 2.3 L
T1 = initial temperature = 28 °C + 273.15 = 301.15 K (converted to Kelvin)
P2 = final pressure (at a depth of 20 m) = 3.0 atm
V2 = final volume (what we need to find)
T2 = final temperature = 15 °C + 273.15 = 288.15 K (converted to Kelvin)
Now, we can substitute the known values into the equation:
(0.90 atm * 2.3 L) / (301.15 K) = (3.0 atm * V2) / (288.15 K)
Next, we can rearrange the equation to solve for V2:
(0.90 atm * 2.3 L * 288.15 K) / (301.15 K * 3.0 atm) = V2
By simplifying and calculating the above expression, we can find the value of V2, which will give us the volume of the balloon at a depth of 20 m.