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Ice on a lake

1. Homework Statement
An ice sheet forms on a lake. The air above the lake is at [tex]\Delta T[/tex] (<0), while the water below the ice sheet is at 0°C. Assume that the heat of fusion of the water freezing on the lower surface is conducted through the sheet to the air above. How much time does it take to form an ice sheet w(t) tick?

The problem has to be solved by means of the microcanonical ensemble.

2. Homework Equations


[tex]\Omega = \int_{\mathcal{H}<E} d^{3N}q d^{3N}p[/tex]
S=k[tex]\log \Omega[/tex]

3. The Attempt at a Solution

In the thermodynamics textbook I found the equation

[tex]\frac{dQ}{dt}=-kA\frac{\Delta T}{w}[/tex],

where k is the thermal conductivity of ice, that after being integrated gives te solution to the problem, but I need to solve it by means of the ideas of statistical physics.

I don't know how to pose the problem in a statistical physics fashion.
 

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