Question

12)  A scuba diver descends to 40 meters below the surface and has a 10 liter tank that contains air at 9 MPa and 7 C.  Assume that the water has a density of 1000 kg/m³and that atmospheric air is 100 kPa.  He breathes at 5 liters/min.  How long can he stay at the 40 meter depth?

Answer should be 34.6 minutes

Answer 1

Pressure at 40 m. below the water surface can be calculated as:

P= Patm + pgh

P= 100+ 1000 x 9.81 x 40 -= 492.4 kPa 1000

Mass of 5 liters of air at 392.4 kPa can be calculated as:

m = PV RT

492.4 x 0.005 m= 0.287 x (7 + 273) = 0.031 kg/min.

Mass of air in 10 L. tank at 9 MPa;

m = PV RT

M= 9000 x 0.010 0.287 x (7 + 273) 79) = 1.12 kg

Thus, time taken to consume all of the air can be calculated as:

11.12 m 0.031 = 36.129 min.