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 4.0o C, and the temperature at the surface is 23.0o 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?
Solution 14E Assume the number of moles of gas in the bubble remains constant. T 1 277 K T 2 296 K a)pv = RT pv T = nR = constant because n and R are constants p1 1 p2 2 T 1 = T 2 v2 p1 T2 v1 = (p2( T1 ) = ( 3.5 atm )(296 K) 1 atm 277 K = 3.74 b)This increase in volume of air in the lungs would be dangerous . If pressure decrease, volume increases