A
container of water has been outdoors in cold weather until a
5.0-cm-thick slab of ice has been formed on
its surface. The air above the ice is at
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Solution: Click For PDF Version
As the
temperature of water inside the tank will be
Data relevant to the problem are
Therefore, rate of heat flow out through the ice slab will be
The rate of
freezing can be calculated by noting that the latent heat of fusion
of water is
Density of
water at
Let
And we know
the amount of heat that is flowing out through
and
Therefore, the rate of formation of ice at the bottom of the ice slab is 0.4 cm per hour.
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We have to calculate the rate of formation of ice
(in centimetres per hour)
on the bottom surface of the ice slab. For the
thermal conductivity and density of ice we may use the values
and
,
respectively. We may assume that no heat flows through the walls of
the tank.
and the outside temperature is
.
The width of the ice slab is 5 cm. The rate of flow of heat from
water in the tank through each unit cross-section of the ice slab
can be calculated from the heat conductivity equation
be
the ice thickness that is formed in one hour. This implies that
amount of heat that is flowing out of the tank in one hour is
of
the ice slab per hour is equal to H.
We, therefore, have the relation
