Liquid water coats an active (growing) icicle and extends up a short, narrow tube along the central axis. 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 `T_(r)` can be below `0^(@)`C. Take L=0.10m and `T_(r)`=`-5^(@)`C.Assume that the central tube and the upward conduction path both have crosse-sectional area A=0.5`m^(2)`. The thermal conductivity of ice is 0.40 W`//mcdotK`, latent heat of fusion is `L_(F)=4.0xx10^(5) J//K` and the density of liquid water is 1000 kg`//m^(3)`.

The rate at which mass converted from liquid to ice at the top of the central tube is

Options

A. `7.5xx10^(-3) kg//s`
B. `2.5xx10^(-5) kg//s`
C. `5xx10^(-3) kg//s`
D. `5xx10^(-5) kg//s`

Answer

B