If the balloon had a volume of 5 L at a depth of 50 m , what was the original volume of the balloon if we assume the pressure at the surface of the water is 14.7 psi?

Question

Underwater pressure increases by 14.7 psi for every 10 m of depth. Standing on a boat in scuba gear, you fill a balloon with helium.

Answer 1

Let us first find the pressure at 50 m, knowing that pressure increases by 14.7 psi every 10 m:

50 m x 14.7 psi/10 m = 73.5 psi increase in pressure

That makes the new pressure at 50 m = original + increase = 14.7 psi + 73.5 psi = 88.2 psi

Now, assuming a constant temperature, we can apply Boyle's Law to find the original volume:

P1V1 = P2V2

P1 = 14.7 psi

V1 = ?

P2 = 88.2 psi

V2 = 5 L

V1 = P2V2/P1 = (88.2)(5)/14.7

V1 = 30 liters