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Liquid water coats an active (growing) i...

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)`.

At what rate does the top of the tube move downward because of water freezing there?

A

`5xx10^(-8) m//s`

B

`2.5xx10^(-3) m//s`

C

`2.5xx10^(-8) m//s`

D

`4.5xx10^(-2) m//s`

Text Solution

Verified by Experts

The correct Answer is:
C
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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

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