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Name: Katherin
Status: student
Grade: N/A
Location: AL
Country: N/A
Date: 1/9/2005


Question:
Why is it true that a cup of boiling water contains less heat than a large iceberg?


Replies:
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


Katherin,

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?

Bob Hartwell


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.

Vince Calder


Katherin,

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
Physics Instructor
Illinois Central College



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