A diving bell is a 3.0-m-tall cylinder closed at the upper end but open at the lower end. The temperature of the air in the bell is 20°C. The bell is lowered into the ocean until its lower end is 100 m deep. The temperature at that depth is 10°C. a. How high does the water rise in the bell after enough time has passed for the air inside to reach thermal equilibrium?

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1. Determine the initial conditions inside the diving bell when it is at the surface. The initial volume of air (V1) can be calculated using the height of the cylinder and its cross-sectional area (A). Assume the pressure inside the bell initially is equal to the atmospheric pressure (P1).
2. Calculate the pressure at the depth of 100 m using the hydrostatic pressure formula P = P0 + \rho g h, where P0 is the atmospheric pressure, \rho is the density of seawater, g is the acceleration due to gravity, and h is the depth.
3. Apply the ideal gas law to find the new volume of air (V2) inside the bell at depth, considering the air is now at a lower temperature (10°C). Use the formula P1V1/T1 = P2V2/T2, where T1 and T2 are the initial and final temperatures in Kelvin.
4. Calculate the new height of the air column inside the bell by dividing the new volume of air (V2) by the cross-sectional area (A) of the bell. This gives the height of the air column after the bell is submerged.
5. Subtract the height of the air column from the total height of the bell to find the height to which the water rises inside the bell.