A diving bell is a 3.4 m -tall cylinder closed at the upper end but open at the

Question

A diving bell is a 3.4 m -tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is 30 C. The bell is lowered into the ocean until its lower end is 100 m deep. The temperature at that depth is 10C.

a)

How high does the water rise in the bell after enough time has passed for the air to reach thermal equilibrium?

Express your answer to two significant figures and include the appropriate units.

b)

A compressed-air hose from the surface is used to expel all the water from the bell. What minimum air pressure is needed to do this?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Given,

h = 3.4 m ; T = 30 deg C = 303 K ; h' = 100 m ; T' = 10 deg C = 283 K

a)We know that

PV = n RT

Patm = 101 kPa

P at 1 m seawater = 10060 Pa

P = 101000 + 100 x 10060 = 1107 kPa = 10.92 atm

H = 3.4 - 101 x 3.4 x 283/303 x 1107 = 3.11 m

Hence, H = 3.11 m

b)P = 1 atm + 10.92 atm = 11.92 atm

Hence, P = 11.92 atm

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