If the balloon had a volume of 2 L at a depth of 40 m, what was the original volume of the balloon if we assume the pressure at the surface of the water is 14.7 psi?
1 Answer
The volume at the surface is 10 L.
Explanation:
The pressure at a depth of 40 m is the hydrostatic pressure of the water plus the atmospheric pressure.
The hydrostatic pressure
#color(blue)(bar(ul(|color(white)(a/a)P = ρghcolor(white)(a/a)|)))" "#
where
∴ The total pressure at 40 m is
Now we can use Boyle's Law to calculate the volume of the balloon at the surface.
#color(blue)(bar(ul(|color(white)(a/a) P_1V_1 = P_2V_2color(white)(a/a)|)))" "#
#V_2 = V_1 × P_1/P_2#
In your problem,
∴