Physics Lab Specific Heat of Solids 1

INTRODUCTION Whenever two objects with different initial temperatures are put in contact with each other, the warmer one will cool down, and the cooler one will warm up, until they reach the same temperature. We now know that this has to do with the motions of molecules: what we sense as temperature is related to the average kinetic energy of the molecules of each material: the faster they’re vibrating around, the hotter the object feels. We can sidestep this molecular picture by dealing with objects as a whole, and treating the energy transfer as the flow of heat, rather than kinetic energy transfer among particles. Experiments have shown that the heat transfer Q = mcΔT, where ΔT = Tfinal-Tinitial of the object you’re considering, m is its mass, and c is referred to as the “specific heat” of the material it’s made up of. For most materials over a wide range of temperatures, c is close enough to a constant value that we will consider it to be exactly constant. Note that a Specific Heat for Various Materials positive Q means that energy flowed into the object (raising Material Specific Heat its temperature), while a negative Q means that energy left (J/kg C°) the object (leaving it at a lower temperature than at the Water 4186 beginning). Also note that you must be careful to associate Aluminum 900 the mass, specific heat, initial temperature, and final Steel 448 temperature, for the appropriate object being considered in Brass 386 any particular calculation, and not some other object. Copper 380 Energy is always conserved, and this is a useful fact when dealing with heat as a kind of energy flow. If we have a perfectly insulating container, then no energy can flow into or out of that container. So, the net heat flow for everything in the container combined Qnet must equal zero. In this particular lab, we will heat up a metal sample, and drop it into a cooler inner calorimeter cup partially filled with water. We will assume that the rest of the calorimeter is perfectly insulating, so that: Qnet = 0, or Qmetal + Qwater + Qcup = 0 If the cup were not perfectly insulating, we would also have to have a term for the heat transfer to the surrounding air, stirrer, outer cup, etc. PROCEDURE 1. Gather all the necessary materials: triple-beam balance, metal samples, calorimeter cup, two temperature sensors or thermometers, metal can, and hotplate. Note: the temperature sensor that you use in your calorimeter must not have blue plastic tubing at the end, but the one you use to measure the temperature of the heated sample may or may not, it does not matter. In either case, never remove the blue plastic tubing from any temperature sensor. 2. Fill the metal can approximately half full of water and start heating it on the hotplate. Note: you want the water to be hot, but not boiling (60-80°C is a good temperature). Also: try to keep the temperature of the water as steady as possible, by keeping the hotplate on a constant setting, and stirring the water occasionally. 3. Measure the mass of the inner aluminum cup only (remove it from the outer cup, and remove the plastic ring) using the triple-beam balance. Note the uncertainty in this mass. 4. Note which metal sample you are using. Then, measure the mass of the metal sample using the triple-beam balance. Note the uncertainty in this mass. Physics Lab Specific Heat of Solids 2

5. Tie a thread to the metal sample, and lower the sample into the metal can, to allow it to heat up. (Keep the end of the thread outside, so that you may pull the metal sample out easily.) Insert a temperature sensor or thermometer into the water in the can, so that you will be able to measure its temperature. 6. At the sink, fill the inner aluminum cup part-way with cool water. You will want enough to completely cover the metal sample (when the sample is lying on its side), but not much more. If you use too much water, the temperature change will be too small to get reliable data. If you use too little, the metal sample will lose significant heat to the surrounding air, and it will be difficult to bring the cup, water, and sample into thermal equilibrium. 7. Measure the mass of the inner aluminum cup (still without the plastic ring), now partially filled with water. Note the uncertainty in this mass. The mass of the water itself will be this new mass, minus the mass you found in step 4. 8. Insert the inner calorimeter cup (now containing water) into the outer calorimeter cup, with the plastic insulating ring separating them. Place the cover over the calorimeter and insert the second temperature sensor or thermometer through the stopper in the top cover. The stirrer should also be inside, going through the hole near the middle of the top cover. Gently stir the water for about a minute. 9. Once the all temperatures are stable, record the initial temperature of the cool water in the calorimeter cup. We will assume that the aluminum inner cup is also at the same temperature. Also record the initial temperature of the metal sample, which we will assume is the same as the temperature of the water in the metal can on the hotplate. 10. Carefully remove the metal sample from the metal can, and quickly remove the cover from the calorimeter. Quickly place the metal sample in the inner calorimeter cup, and confirm that it is indeed fully submerged. Quickly re-cover the calorimeter. (Remember, we want no heat to escape to the outside air.) 11. Gently stir the water until the water and metal specimen reach a final equilibrium temperature. (You can confirm this by moving the temperature sensor around, looking for “hot spots” or “cool spots.” Generally, as long as your temperature sensor is not near a “hot spot,” the equilibrium temperature will likely be your highest reading. This is because the calorimeter is not actually a perfect insulator, so the heated parts will lose heat to the room, desk, etc.) Record the final equilibrium temperature, with its uncertainty. (Note: much of this uncertainty will be due to the fact that your “final” temperature is a judgment call, made when you guess that everything has first reached equilibrium.) 12. Repeat steps 4-11 for the remaining metal samples.

Plastic Tubing Physics Lab Specific Heat of Solids 3

ANALYSIS

1. Calculate Qwater and Qcup for each case. Note: you will need to use the accepted values for the specific heats of water and aluminum for these calculations. 2. Using the results of the previous step and the mass and change in temperature of each metal sample, calculate the specific heat of each metal sample. 3. Calculate the % error for each metal sample, using the value in the textbook as the accepted measured accepted value. Remember: the equation for % error is: %error  accepted 100% . 4. Using your uncertainties, calculate a worst-case maximum and minimum specific heat for at least one metal sample. RESULTS Your results section should be a table, indicating each type of material, its accepted specific heat, its experimental specific heat (with uncertainty, if applicable), and the % error. QUESTIONS 1. List as many of the assumptions made in this experiment that you can think of. Based on your experimental results, do you think that these assumptions were valid? Why or why not? 2. Why must the water in the inner cup be gently stirred during this experiment? Also, why stir at all? 3. In step 10, if some drops of water are accidentally transferred along with the sample as it is placed into the calorimeter, will this result in the specific heat measured being too large or too small? Why? 4. Do the %error results you found surprise you, for any or all of your metal samples? Why or why not? 5. Do the accepted values fall within the experimental range of values (a “range” because of the uncertainty)? If not, then your measurements may have been wrong, your calculations may have been wrong, or you may have estimated too little uncertainty. Try to figure out what was the actual cause, in your case. EXTRA CREDIT (Optional) For up to 3 points, design and perform a new experiment to find the specific heat of aluminum, without using the aluminum sample (and without assuming that you already have a value for it from any other source). Use only the equipment used here in this lab. Be sure to describe your procedure and calculations clearly. (Note: you are allowed to use the accepted value for the specific heat of water.)