There is a tendency to believe that any time heat is flowing into ice, the ice is melting.
NOT SO. When heat is flowing into ice, the ice will be melting only if the ice is
already at the melting temperature. When heat is flowing into the ice that is below
the melting temperature, the temperature of the ice is increasing.
As mentioned in the preceding chapter, there are times when you bring a hot object into contact
with a cooler sample, that heat flows from the hot object to the cooler sample, but the
temperature of the cooler sample does not increase, even though no heat flows out of the cooler
sample (e.g. into an even colder object). This occurs when the cooler sample undergoes a phase
change. For instance, if the cooler sample happens to be H2O ice or H2O ice plus liquid water, at
0°C and atmospheric pressure, when heat is flowing into the sample, the ice is melting with no
increase in temperature. This will continue until all the ice is melted (assuming enough heat
flows into the sample to melt all the ice). Then, after the last bit of ice melts at 0°C, if heat
continues to flow into the sample, the temperature of the sample will be increasing 1.
Lets review the question about how it can be that heat flows into the cooler sample without
causing the cooler sample to warm up. Energy flows from the hotter object to the cooler sample,
but the internal kinetic energy of the cooler sample does not increase. Again, how can that be?
What happens is that the energy flow into the cooler sample is accompanied by an increase in the
internal potential energy of the sample. It is associated with the breaking of electrostatic bonds
between molecules where the negative part of one molecule is bonded to the positive part of
another. The separating of the molecules corresponds to an increase in the potential energy of
the system. This is similar to a book resting on a table. It is gravitationally bound to the earth.
If you lift the book and put it on a shelf that is higher than the tabletop, you have added some
energy to the earth/book system, but you have increased the potential energy with no net increase
in the kinetic energy. In the case of melting ice, heat flow into the sample manifests itself as an
increase in the potential energy of the molecules without an increase in the kinetic energy of the
molecules (which would be accompanied by a temperature increase).
The amount of heat that must flow into a single-substance solid sample that is already at its
melting temperature in order to melt the whole sample depends on a property of the substance of
which the sample consists, and on the mass of the substance. The relevant substance property is
called the latent heat of melting. The latent heat of melting is the heat-per-mass needed to melt
the substance at the melting temperature. Note that, despite the name, the latent heat is not an
amount of heat but rather a ratio of heat to mass. The symbol used to represent latent heat in
general is L, and we use the subscript m for melting. In terms of the latent heat of melting, the
amount of heat, Q, that must flow into a sample of a single-substance solid that is at the melting
temperature, in order to melt the entire sample is given by:
1 In this discussion, we are treating the sample as if it had one well-defined temperature. This is an approximation.
When the sample is in contact with a hotter object so that heat is flowing from the hotter object to the sample, the
part of the sample in direct contact with and in the near vicinity of the hotter object will be at a higher temperature
than other parts of the sample. The hotter the object, the greater the variation in the temperature of the local bit of the sample with distance from the object. We neglect this temperature variation so our discussion is only
appropriate when the temperature variation is small.
2
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