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Chapter 3: Q14E (page 610)

A diver 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 4.0°C, and the temperature at the surface is 23.0°C. (a) What is the ratio of the volume of the bubble as it reaches the surface to its volume at the bottom? (b) Would it be safe for the diver to hold his breath while ascending from the bottom of the lake to the surface? Why or why not?

Short Answer

Expert verified

(a) Ratio is 3.74

(b) No, it will get dangerous as the air in the lungs will expand at the factor of 3.74 , which can cause the lungs to explode.

Step by step solution

01

Step: 1 Ideal Gas Equation

Applying the ideal gas equation

PV = nRT

Here, P=Pressure of gas, V=Volume, n=no. of moles, R = 8.314472 J/mol

K=Ideal gas constant, T=temperature of gas

02

Step: 2 Calculation

PV=nRTV=nRTPV1→atbottomV2→atsurfaceV2V1=nRT2/P2nRT1/P1V2V1=T2P1T1P2V2V1=(23+273.15)K(3.5)atm(4+273.15)K(1)atm=3.74

Hence, the ratio is 3.74

03

Step: 3

No, it will get dangerous as the air in the lungs will expand at the factor of 3.74, which can cause the lungs to explode.

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