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