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A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is...

A solid spherical shell with a 12.0 cm inner radius and 15.0 cm outer radius is filled with water.
A heater inside the water maintains the water at a constant temperature of 350 K. The outer
surface of the shell is maintained at 280 K. The shell is made of Portland cement, which has a
thermal conductivity of 0.29 W/(mK).
(a) Starting from the basic equation for thermal conduction, derive the rate at which heat flows
out of the water. Derive a symbolic result first, and then substitute to get a numerical answer.
(b) The heater is turned off at time t = 0. How much time elapses between the time the heater is
turned off and the time the water cools to 330 K? Obtain your result starting from the basic
equation for thermal conduction.

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genius_generous answered 2 years ago
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