Liquid water coats an active (growing) icicle

and extends up a short, narrow tube along the central axis

(Fig. 18-54). Because the water – ice interface must have a temperature

of 0°C, the water in the tube cannot lose energy through

the sides of the icicle or down through the tip because there is no

temperature change in those directions. It can lose energy and

freeze only by sending energy up (through distance L) to the top

of the icicle, where the temperature Tr can be below 0°C. Take

L
0.12 m and Tr
5°C. Assume that the central tube and the

upward conduction path both have cross-sectional area A. In

terms of A, what rate is (a) energy conducted upward and (b)

mass converted from liquid to ice at the top of the central tube? (c)

At what rate does the top of the tube move downward because of

water freezing there? The thermal conductivity of ice is 0.400

W/m

K, and the density of liquid water is 1000 kg/m3.