1. A primitive diving bell consists of a cylindrical tank with one end open and
ID: 1731049 • Letter: 1
Question
1. A primitive diving bell consists of a cylindrical tank with one end open and one end closed. The tank is lowered into a freshwater lake, open end downward. Water rises into the tank, compressing the trapped air, whose temperature remains constant during the descent. The tank is brought to a halt when the distance between the surface of the water in the tank and the surface of the lake is 19.0 m. Atmospheric pressure at the surface of the lake is 1.01 x 105 Pa. Find the fraction of the tank's volume that is filled with air.
2. A tube has a length of 0.014 m and a cross-sectional area of 5.1 x 10-4 m2. The tube is filled with a solution of sucrose in water. The diffusion constant of sucrose in water is 5.0 x 10-10 m2/s. A difference in concentration of 7.8 x 10-3 kg/m3 is maintained between the ends of the tube. How much time is required for 8.7 x 10-13 kg of sucrose to be transported through the tube?
Explanation / Answer
Given,
The distance between the surface of the wate and surface of the lake, h = 19 m
The Atmospheric pressure at the surface of the lake, Psurface = 1.01 x 105 Pa
The density of the water, ? =1000kg/m3
The acceleration due to gravity, g = 9.8m/s2
Now finding the absolute pressure at a depth h is
ph = psurface + ?gh
= 1.01 x 105 Pa + (1.00*103 kg/m3)(9.8 m/s2)(19 m) = 2.87 x 105pa
From the Boyle' law we can write as
Vh/Vtank = Psurface/Ph = 1.01 x 105 Pa/(2.87 x 105pa) = 0.352
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