Question

jack is snorkelling in tropical warms with great visibility . he spots his friends at the bottom of the reef scuba diving they wave him down to show him a turtle . jack did not relise that he managed to dive 20 m deep and is quickly running out of fair- his friends offer him air from the scuba diving regulator which gives air under ambient pressure at 20 m depth . jack fills his lungs completely (5 l capacity) with air from the regulator and ascends to the surface holding his breath . what would the volume of jacks lung be when he reaches the surface according to boyle's law?

a) 10 L

b) 15 L

c) 5 L

d) 20 L

Answer 1

(b) 15 L

According to Boyle's law, pressure (P) is inversely proportional to volume (V). Hence, PV = constant.

We have, P1 = P_atm + hDg, V1 = 5L, P2 = P_atm,, V2 = ?

where, h = depth of water = 20m, D = density of water = 1000 kg/m³, g = 9.8m/s², P_atm = 10⁵ Pascal

Applying Boyle's Law, P1V1 = P2V2

Therefore, V2 = (P1V1) / P2 = ([10⁵+{20x1000x9.8}] x 5) / 10⁵ = ([10⁵+{1.96x10⁵}] x 5) / 10⁵ = ([2.96x10⁵] x 5) / 10⁵ = 14.8L

Hence the volume of Jack's lung when he reaches the surface according to Boyle's law is 15L.