A diver named Jacques observes a bubble of air rising from the bottom of a lake

Question

A diver named Jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). The temperature at the bottom is 4.00 C, and the temperature at the surface is 23.0 C.

Part A: What is the ratio of the volume of the bubble as it reaches the surface (Vs) to its volume at the bottom (Vb)?

Part B: If Jacques were to hold his breath the air in his lungs would be kept at a constant temperature. Would it be safe for Jacques to hold his breath while ascending from the bottom of the lake to the surface?

Explanation / Answer

b) at point A

field due to top wire is B1 = mu_o*i1/(2*pi*r) = (2*10^-7*17.9)/(0.05) = 7.16*10^-5 T out of the page

Field due to bottom wire is B2 = mu_o*i2/(2*pi*r) = (2*10^-7*6)/0.05 = 2.4*10^-5 T out of the page

B = B1+B2 = (7.16+2.4)*10^-5 = 9.56*10^-5 T out of the page

using ideal gas equation

P1*V1/T1 = P2*V2/T2

(1*Vs/(273+23)) = (3.5*Vb/(273+4))

Vs/Vb = (273+23)*3.5/(273+4) = 3.74

B) No,it would not be safe at this highest ratio

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