Heat, Temperature, and Thermal Energy
Why is it true that a cup of boiling water contains less
heat than a large iceberg?
The energy stored in ice is related to the transition from water to ice.
The process requires energy which is approximately 80,000 calories per
liter. Boiling water also has a transition from water to steam but the
value per liter is 540,000 calories. For one liter of boiling water
compared to one liter of ice, the energy stored in the steam is nearly 7
times more per liter. An iceberg is huge compared to a cup of water, thus
the energy stored is much greater.
Dr. Harold Myron
The simplest answer is that the iceberg has such a large mass when
compared to the cup of boiling water.
Heat = mass * Cp * change in temperature
If we lower the temperature of the iceberg 1 degree (say from 10 F to 9 F)
the amount of heat removed would be large due to the very large mass.
For the cup of water (mass 0.52 pounds) the change in temperature is
large (212-32 = 180 F) and there would be heat released from the latent
heat of fusion and some additional heat lowering the now cup of ice from
32F to 9F. The total amount of heat released however is small simply
because the mass is so small.
Here is something for you to do at home. Start with the cup of boiling
water. I have given you the mass and the temperature changes. Calculate
the heat released from 212F to 32F, then add the heat released due to
the latent heat of fusion, then add the heat released from the
temperature change of the ice from 32F to 9F. Taking the total heat
released, calculate the mass of an iceberg such that the total heat
released from the boiling cup of water is enough to raise the iceberg
from 9F to 10F. What is the mass of the iceberg?
It is not a good mental picture to think of "heat" as an invisible fluid
that a body can hold. The question "How much heat does a body contain?"
really has no meaning. Heat is the random vibrations of atoms and
molecules, if the atoms and molecules vibrate more the temperature
increases. But that does not mean that the body "contains more heat", it
means the atoms and molecules are vibrating with more energy. What may be
confusing to you is the fact that there is a function -- unfortunately
called the "heat content" -- which is adds up the amount of heat required
to heat a substance from one temperature to another temperature. So for
example if we cooled a mol of water (18 gm = 18 ml) to very low
temperature -- say about -273 C (or just above absolute zero 0 kelvins) and
begin to heat it in a calorimeter (a device for measuring the amount of
heat required to increase the temperature of a substance and/or to measure
the heat required to melt/boil a substance) and if we keep track of the
amount of electrical energy we feed into the sample warming it up to 0 C
(=273.15 kelvins) then how much electrical energy it takes to melt the
sample, then how much electrical energy it takes to heat the sample from 0
C to 25 C=298 kelvins, and we add all the joules we fed into the
calorimeter, this amount of energy: (H298 - H0) is called the "heat
content". It is an unfortunate accident of history why the name is what it
is. It is clear however that if we did the same experiment mentally on a
cup of hot water and an iceberg, the iceberg would require more energy
input than the cup of tea -- because the amount of water in the iceberg is
many times that contained in the hot cup of tea.
An iceberg contains more heat than a cup of boiling water because it is so
gigantic. An iceberg can have more than fifty million cups of ice in it.
Although the amount of heat energy in a cup of ice is very small, fifty
million of these cups can have a great deal of heat.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012