| | Essential questions | | What is the difference between temperature and heat?
How does the specific heat differ between water and steel? | |
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In everyday conversation we often use the words heat, thermal energy, and temperature interchangeably. In physics, however, they are different (albeit related) quantities. Temperature is the measure of the average kinetic energy per atom or molecule. Thermal energy is the total energy a substance contains. Heat is the flow of thermal energy from a hotter to a colder material. In this investigation you will see that water and steel contain very different amounts of thermal energy for the same mass—even though they are at the same temperature. 
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Specific heat of steel
Materials: You will need two foam cups (8 oz or larger), water, a hot plate (or very hot water from tap), ice, a mass scale, 10 or more steel washers (m ≥ 100 g), string, a Celsius thermometer (or other temperature probe), a ring stand, and a clamp. - Tie the steel washers together with the string.
- Tare (or zero) the scale with one of the empty foam cups. Measure the mass of the steel washers. Choose a number of steel washers that will have a total mass close to 100 g.
- Cover the washers with ice and cold water. Allow to equilibrate close to the freezing point. Measure the temperature of the cold water.
- Mount the foam cup in the ring stand and ring clamp.
- Heat water in an appropriate container using a hot plate.
- Measure 100 g of hot water into the other foam cup. Measure the temperature of the water.
- Quickly move the steel washers from the ice water into the hot water. Stir them for a minute or two until the temperature equilibrates. Measure the final temperature of the water.
- Repeat the experiment by adding 100 g of ice water to the cup containing 100 g of hot water.
- Which caused a larger change in the temperature of the hot water, the 100 g of 0°C steel or the 100 g of 0°C ice water?
- Which material do you think has a higher specific heat, steel or water? Why?
- Calculate the specific heat of steel from your data given the specific heat of water: cwater = 4.18 J/(g °C) = 4,180 J/(kg °C). Ask your teacher for the correct value—or look it up in an authoritative reference book, such as the CRC Handbook of Chemistry and Physics. Was your calculation correct?
- Approximately equal masses of hot water and cold steel were mixed, yet the final temperature is not halfway between the two temperatures. Why not?
- Now imagine you are given an unknown metal. Explain very specifically and in detail how you would design an experiment to determine whether the unknown metal is steel.
- How did the distribution of energy between the washers and water change during the experiment?
- What would happen to the final temperature if you put twice as many (i.e., 200 g) cold steel washers into the water? How does the final temperature depend on the relative mass of the steel and water?
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Deriving the specific heat of steel from the investigation
The amount of thermal energy in a material is defined by the specific heat equation: where m is the mass of the material, cp is the specific heat of the material, and ΔT is the difference in temperature between the material and a reference temperature. In this investigation, we will use the temperature T0 of the ice water, which should be close to 0°C, as the reference temperature. The steel washers gained thermal energy when they changed temperature from T0 to T1, while the hot water lost an equal amount of thermal energy when it changed temperature from T2 to T1.
The change in the thermal energy of the steel was The change in the thermal energy of the hot water was To solve this problem, set the thermal energy gained by the steel washers equal to the thermal energy lost by the hot water: Use algebra (and show your work) to solve this equation for the unknown quantity csteel (the specific heat of steel). 
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Proper handling of mercury thermometers
Proper handling of mercury thermometers. In conducting the investigation, you might be using a mercury thermometer. Be careful in handling these kinds of thermometers, because mercury can be toxic if the thermometer breaks. Do not bend the thermometer, place anything on top of it, or leave it in a location where it can be knocked over easily.
Should the thermometer break and spill its mercury, the Environmental Protection Agency (EPA) provides the following guidelines: - Have everyone else leave the area; don’t let anyone walk through the mercury upon exiting. Make sure all pets are removed from the area. Open all windows and doors to the outside; shut all doors to other parts of the building.
- Do not allow children to help you clean up the spill.
- Mercury can be cleaned up easily from the following surfaces: wood, linoleum, tile, and any similarly smooth surfaces.
- If a spill occurs on carpet, curtains, upholstery, or other absorbent surfaces, these contaminated items should be thrown away in accordance with the appropriate disposal means. Only cut and remove the affected portion of the contaminated carpet for disposal.
Your teacher should have safety and hazardous material instructions for how he or she will go about cleaning up the spilled mercury.
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What never to do with a mercury spill
The EPA also offers instructions on what not to do in the event of a mercury spill: - Never use a vacuum cleaner to clean up mercury. The vacuum will put mercury into the air and increase exposure.
- Never use a broom to clean up mercury. It will break the mercury into smaller droplets and spread them.
- Never pour mercury down a drain. It may lodge in the plumbing and cause future problems during plumbing repairs. If discharged, it can pollute the septic tank or sewage treatment plant.
- Never wash clothing or other items that have come in direct contact with mercury in a washing machine, because mercury may contaminate the machine and/or pollute sewage. Clothing that has come into direct contact with mercury should be discarded. By “direct contact,” we mean that mercury was (or has been) spilled directly on the clothing, for example, if you break a mercury thermometer and some of elemental mercury beads came in contact with your clothing.
- Never walk around if your shoes might be contaminated with mercury. Contaminated clothing can also spread mercury around.
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