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Revised: Jan. 22, 2002
EXPERIMENT 1:
A THERMAL MODEL OR ANALOG
Introduction
One of the most difficult things about the relationship between heat
and temperature is to understand that when heat is added to a body, the
temperature rises, and that the amount of the temperature change depends
on the amount of material in the body. This experiment attempts to address
this problem.
The approach taken in this experiment is to use a model or analog of
an experiment that uses heat (see Experiment
2).
There are three components of our model: the water volume which represents
heat mass; the food dye, which represents the heat added to the heat mass;
and the color of the water in the heat mass which represents the temperature
of the heat mass.
The water (or heat mass) is the “container” which holds the
heat. The larger the volume of water (i.e., “heat mass”),
the less color change (i.e., “temperature”) that will occur
in the water for a given amount of color (i.e., “heat”).
From what happens to the color of the water after we add food coloring,
we can deduce what will happen to the heat-mass temperature, if we add
heat to the heat mass.
Most people will agree immediately that, if we add a given amount of
food coloring to a small volume of water, the water will become a deeper
red in color than if we add the same amount of food coloring to a much
larger volume of water.
Once we accept the analogies among water volume, amount of food coloring,
and color of the water, it is easy to conclude that if we add a given
amount of heat to a small heat mass, the temperature of the heat mass
will rise further than if we add the same amount of heat to a much larger
heat mass.
In our analogy, the food coloring (coming from a bottle) represents the
heat added to the water; in the heat/temperature system that we want to
understand, the heat (analogous to food coloring) comes from a hot plate,
a stove, the Sun, or another source of heat.
Equipment needed
Two cups with at least a 500 ml capacity
one 2-liter soda bottle
one squeeze bottle of red food coloring
a thermometer or temperature probe connected to a computer
Procedure 1: Analog of adding heat to cold water
Put 250 ml of water in the two cups, and put 1 liter of water into the
2-liter bottle.
Put 20 drops of food coloring in each of the three vessels and stir till
the food coloring is dispersed throughout the water.
Compare the color of the water in each vessel with that in the other
two. The students should note that 20 drops in each of the cups produces
a liquid with a deep-red color; while 20 drops in the soda bottle produces
only a light-pink color—that happens because the same amount of
coloring goes into four times the water in the bottle than in the cups
and is more diluted.
The analogies here are: volume of water in the vessel with the heat mass
(related to volume) of an object; amount of food coloring dropped into
the water with the amount of heat put into the heat mass; and, the color
of the water after food coloring is added with the temperature of the
water. If we had put 10 teaspoons of hot water into the 250-ml cups and
10 in the soda bottle, the water temperature in each cup would have increased
significantly and would have increased to the same value; while the temperature
of the water in the soda bottle would have increased only slightly. (Another
analogy which may be of help to the students—put two teaspoons of
sugar into 250 ml of water, stir till dissolved; then put two teaspoons
of sugar into 1 liter of water. Taste the two solutions. The water in
the 250-ml cup will taste sweet, while that in the 1-liter bottle will
hardly taste different than tap water.)
This is an analog of putting a container of water on a hot plate to put
heat into it.
Procedure 2: Analog of adding cold water to hot water
Fill one cup with 500 ml of water and add 20 drops of red food coloring.
Pour this into the soda bottle. Refill the cup with 500 ml of water ,
add 20 drops of red food coloring, and pour 250 ml of the mixture into
the other cup.
Empty the first cup and rinse with clear water. Fill it with 250 ml of
clear water and empty into the cup with food coloring in it. Refill with
250 ml of clear water and empty into the soda bottle.
Stir the water in the cup and the bottle until thoroughly mixed. Compare
the color of the water in the two containers. The water in the soda bottle
will be darker in color than that in the cup because we only increased
the total volume of water in it by 50 %; while, in the cup, we doubled
the total volume.
The analogies here are: clear water is analogous to cold water; colored
water is analogous to hot water; the color of the water is analogous to
the temperature of the water (the darker the color, the hotter the water).
This procedure is analogous to pouring cold water into hot water.
Procedure 3: Analog of adding hot water to cold.
Fill one cup with 250 ml of clear water and fill the soda bottle with
500 ml of clear water. Fill the remaining cup with 500 ml of clear water
and add 20 drops of red food coloring.
Pour 250 ml of the colored water into the soda bottle and pour the other
250 ml into the other cup. Stir till the color has mixed thoroughly. Compare
the colors of the water in the two containers. Now, the water in the soda
bottle will be less dark than that in the cup, because we have increased
the volume of water in the soda bottle by 50 %, while in the cup we have
doubled the total volume.
The analogies here are the same asd those in Procedure 2 above, except
that we are adding colored water (analogous to hot water) to clear water
(analogous to cold water).
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