Hard work
Question: It is well known that water expands when it freezes, which is why
frozen pipes burst. This means that water can do work as it freezes. Where does
the energy come from for this to happen? This is especially puzzling considering
that energy is being removed from the water in order to freeze it.
Answer: The answer is in the question. When water freezes, it releases
significant amounts of energy, called latent heat. If the water is in a pond,
this energy flows into the surrounding air as heat. But if the water is trapped
inside a copper pipe, some of this energy is used to burst the pipe so the water
can expand. This means there is less energy available to flow into the
surroundings in the form of heat.
The confusion perhaps arises because of the term 鈥渓atent heat鈥�, which implies
that the energy has to be lost in the form of heat and not in any other form.
This is not the case.
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Alan Williams-Key
Chelmsford, Essex
Answer: When anything freezes, it drops to a lower energy state because heat
energy, Q, has flowed out of it. In addition, water, which expands on
freezing, pushes against its surroundings doing work, W, which is equal
to the pressure, P, multiplied by the increase in volume, dV.
Hence its internal energy, U, becomes even lower than if it had not
expanded. The change in internal energy, dU, from its original state
can be written as:
dU = 鈥� Q 鈥� W = 鈥� Q
鈥� PdV
This loss of the water鈥檚 internal energy is matched by the gain in the energy
of the surroundings due to the heat and work. Therefore, water doing work as it
freezes does not break the first law of thermodynamics (conservation of energy)
even though heat energy has also been simultaneously removed.
In the case of the broken pipe, the work done is lost. Therefore the amount
of heat required to re-melt the ice should actually be slightly greater than the
amount of heat removed to freeze it in the first place. This is because as the
water expanded it pushed against a much higher pressure when it stretched the
metal pipe than the pressure of the atmosphere pushing on it as it shrinks back
to liquid water. More work was done by the water on the pipe during expansion
than is done by the atmosphere on the water during compression.
In contrast, water in an open container (or sealed in a perfectly elastic
rubber bag) requires exactly the same amount of heat to re-melt as was removed
during freezing since the pressure being worked against is the same in both
directions.
I am not aware, however, if this particular experiment has ever been
performed.
Simon Iveson
Department of Chemical Engineering, University of Newcastle,
New South Wales
We don鈥檛 know if this experiment has been done either, but the next reader
suggests a way of designing an 鈥渋ce鈥� engine that tries to exploit the work done
in expansion鈥擡d
Answer: In order to build an engine based on freezing water, you would need a
heat source, a heat sink and some means of harvesting the work available from
expansion. This is no different in principle to any other type of heat
engine.
The first type of steam engine to enter commercial use was the Newcomen
engine, which was a beam engine used to pump water out of mines. It worked on
the principle of allowing a cylinder to fill with steam at atmospheric pressure,
closing the valve and spraying in water in order to condense the steam.
Atmospheric pressure then pushed the cylinder down and provided the work output
for the pumps. At the end of the stroke, the valve was reopened and steam
re-entered the cylinder, allowing a counterweight to restore the engine to the
original state. The interesting thing, from the point of view of this query, is
that the work is actually done while the system is being cooled鈥攖he
working fluid is contracting rather than expanding.
This raises the question of how efficient an ice engine might be. If the
engine has a cylinder filled with liquid water, and the ice moves a piston up as
it freezes, work could be extracted during that part of the cycle. The ice would
then need to be re-melted in order to return to the starting state and begin the
next cycle. In order to extract as much work as possible, the pressure resisting
the volume expansion must be high. If the moving parts were built to resist 100
atmospheres, then the work extracted from a cubic metre of ice expanding by 9
per cent would be about 900 kilojoules. This is less than 3 per cent of the heat
that must be extracted in order to freeze the ice (or provided to re-melt it),
so the engine would be very inefficient.
Richard Hann
Ipswich, Suffolk
That still leaves us with the question of why water expands close to the
freezing point, in contrast with other liquids鈥擡d
Answer: Normally, when a liquid freezes it contracts slightly as the
molecules move closer together. However, while water contracts as it is cooled
down to 4 掳C, if it is cooled below this temperature, it begins to
expand.
Because of the different electronegativity of the hydrogen and oxygen atoms,
each water molecule is polarised. When two molecules come close enough, there is
an electrostatic attraction between a positively charged hydrogen atom on one
molecule and a negatively charged oxygen on another, leading to the formation of
a hydrogen bond (H-bond). This is the strongest type of intermolecular bonding
and is seen when hydrogen is covalently bonded to one of the highly
electronegative elements: fluorine, oxygen or nitrogen. These compounds have
much higher melting and boiling temperatures than would be expected simply from
trends in the periodic table.
As water cools to 4 掳C, it reaches its maximum density. The liquid
contracts due to reduced molecular motion, and H-bonds can form in greater
quantity. These H-bonds are long and tend to force the two hydrogen atoms on a
water molecule away from each other. Forcing the molecules further apart reduces
the density of the liquid. Because there are fewer molecules in a given volume
when water freezes, it subsequently expands by about 9 per cent.
Reena Patel
Richmond, Surrey
(This answer is dedicated to the memory of my late grandfather
Shiveharandas A. Desai)