To measure how far below the ocean surface a bird dives to catch fish, a scienti

Question

To measure how far below the ocean surface a bird dives to catch fish, a scientist uses a method first devised by Lord Kelvin. He dusts the inside of a plastic tube with powdered sugar and then seals one end. He catches a bird in its nest and attaches the tube to its back, with the open end towards the front. The next night he re-catches the same bird and removes its tube. In one trial, using a 7.0 cm long tube, water has washed away the sugar over a distance of 3.1 cm measured from the open end. Find the greatest depth to which the bird dived while carrying the tube, assuming that the air in the tube remained at a constant temperature

Explanation / Answer

I would use ideal gas law P1V1/T1 = P2V2/T2
where T1 = T2
Initially the air in the tube is at atmospheric pressure P(o) and Volume = volume of tube. Tube has constant. cross section "A" and length "h(o)"
P1V1 = P(o)Ah(o) = P(o)A(7.0)

Underwater the air is under pressure, P2 = P(o) + DgL
This shrinks the column of air to new volume, V2 = A(h(o) - 3.1)
P2V2 = P(o)A(3.9) + DgLA(3.9)

Equate these PV's and solve for "L"
L = P(o)(3.10)/Dg(3.9)
Use P(o) = 1.013x10^5 Pa and D= 1030 kg/m^3 for sea water
L = 7.97 m

The greatest depth to which the bird dived while carrying the tube is around 8m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.