A cylindrical diving bell3.5 m indiameter and 4.4 m tall with an open bottom is

Question

A cylindrical diving bell3.5 m indiameter and 4.4 m tall with an open bottom is submerged to a depth of 160m in the ocean. The temperature of the air at the surface is21?C, and theair’s temperature 160m down is 5.8?C. The density of sea wateris 1025 kg/m3. The acceleration ofgravity is 9.81 m/s2 . How high does the sea water rise in the bell when the bellis submerged? Answer in units of m. A cylindrical diving bell3.5 m indiameter and 4.4 m tall with an open bottom is submerged to a depth of 160m in the ocean. The temperature of the air at the surface is21?C, and theair’s temperature 160m down is 5.8?C. The density of sea wateris 1025 kg/m3. The acceleration ofgravity is 9.81 m/s2 . How high does the sea water rise in the bell when the bellis submerged? Answer in units of m.

Explanation / Answer

original volume =   A * h =  A * 4.40 m . Original temp =   21 + 273 = 294K . original pressure = 1 atm = 101300Pa . Final volume = A * h . Final temp = 273 + 5.8 = 278.8 K . Final pressure = po + gd =101300 + 1025 * 9.81 * 160 =   1710140 . Ideal gas law:       final   pV/T =   initial pV/T .         1710140 * A*h / 278.8   = 101300 * A * 4.4 / 294 . h =    0.247 m         this is theheight of the air, so the water rises   4.4 -0.247 =    4.153meters

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