Thermal Energy.

Labs written for the CARA Space Explorers, Fall 1993

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This is meant to be handed out to the students.*

The smallest unit of aluminum, for example, is one atom of aluminum. Pure aluminum is made up of atoms of aluminum that are not organized into more complicated molecules. In one standard aluminum paper clip, there are about 10,000,000,000,000,000,000,000 atoms. Staighten out a paper clip and cover up half of it. Then cover up half of what's left. Do that two more times. There are still 800,000,000,000,000,000,000 atoms in the little piece of wire that is left. Imagine a piece of paper clip that is 10 times small than that. This tiny piece of aluminum still contains 80,000,000,000,000,000,000 atoms. No wonder it is hard to imagine their existance!

These atoms and molecules are not sitting still. Even the molecules in the desk are vibrating. They are so tiny, and there are so many of them in the desk, that you never see this microscopic movement of molecules. You can notice these tiny vibrations, however, from the object's temperature. The higher the temperature, the faster the atoms and molecules vibrate. When you feel a warm cup of tea, you are feeling the vibrations of the warm teacup starting to vibrate the molecules in your own hand.

We have already discussed kinetic energy and gravitational potential energy. The energy in these vibrations is a third type of energy called thermal energy. You can convert kinetic energy to thermal energy by rubbing your hands together. You put move your hands (kinetic energy), and that energy is converted to thermal energy through a process called friction. You can feel the temperature of your hands rise. So, we can measure the amount of thermal energy in a substance using temperature.

Since each substance has different properties, the amount of energy required to raise its temperature one degree is different. Written as an equation,

energy = m C (T - T)

where m is the mass of the object, T is the temperature before the energy was put in, and T is the temperature after the energy was put in. We will call C the heat capacity (this is a different number for each substance). Just as its name implies, the heat capacity is larger for substances that store more energy. It takes more energy to heat a substance with a large heat capacity. The heat capacity of water at room temperature is defined to be 1 calorie per gram-° C. The heat capacity of other substances can be found by comparison with water, as we will do in this lab.

1. Fill a thermos with about 100 grams of room temperature water. Do this by putting the thermos on the scale, and adding water until the thermos plus water is 100 grams heavier than the thermos.

actual mass of water: ___________________

2. Measure the temperature of the water in your thermos.

______________ ° C

3. Measure the temperature of the water in the hot water bath with _your_ thermocouple (each thermocouple is a little different). This will be same as the temperature of the copper.

______________ ° C

4. Lift one or two pieces of copper from the water bath and place them carefully in the thermos. Put the lid on the thermos so that the heat does not escape. This operation should be done quickly so that the temperature of the copper doesn't change between the time it is in the water bath and the time it is in the thermos.

5. Wait a while (like ten minutes) until the temperature of the water in the thermos stops changing and the temperature of the water and the copper are in equilibrium with each other. Then, measure the final temperature of the water in the thermos.

______________ ° C

6. Measure the mass(es) of the piece(s) of copper you used.

______________

7. The energy that left the piece of copper should equal the energy that went into the water. So,

mwater Cwater (T2water-T1water) = mcopper Ccopper (T1copper-T2copper)

Using the numbers that you measured in this lab plus the fact that

Cwater = 1 calorie/(gram-° C),

calculate the heat capacity of copper, Ccopper.

The heat capacity of copper is:

__________________________________________________

2. If the heat capacity of copper is 0.1 calorie/(gram-° C), how much energy does it take to raise the temperature of 1000 grams of water from room temperature (25° C) to the boiling point of water (100° C - not the boiling point of copper!!)?

3. Assume there is a 1000 gram piece of copper at 80° C and 100 grams of water at 20° C. If the water and copper were put into a thermos and allowed to come to equilibrium, what temperature would they be?

4. Assume we have one thermos with 50 grams of water at 20° C and one thermos with 50 grams of water at 100° C. If we mixed them together, we would have 100 grams of water in a thermos. What temperature would that water be?

5. When you apply pressure to the brakes on you bike, they heat up. So, the thermal energy in the brake pads increased. Where did the energy come from?

**Important Disclaimers and
Caveats**

Go back to the Chicago Fall 1993 Energy home page.