Physics Lab Heat of Fusion 1 INTRODUCTION If there are no phase changes, then 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. However, some heat (energy) is required in order to cause a change in the phase (solid, liquid, or gas) of an object. During the phase change, the temperature of the object does not change at all, even though it is gaining or losing energy (depending on the type of change). Experiments have shown that, in the absence of phase changes, the heat transfer Q = mcΔT, where ΔT = Tfinal-Tinitial of the object you’re considering, m is Specific Heat for Various Materials (Approximate) its mass, and c is referred to as the “specific heat” of the Material Specific Heat material it’s made up of. For most materials over a wide (J/kg C°) range of temperatures, c is close enough to a constant value Water 4186 that we will consider it to be exactly constant. Note that a Aluminum 900 positive Q means that energy flowed into the object (raising Steel 448 its temperature), while a negative Q means that energy left Brass 386 the object (leaving it at a lower temperature than at the Copper 380 beginning). Also note that you must be careful to associate the mass, specific heat, initial temperature, and final temperature, for the appropriate object being considered in any particular calculation, and not some other object. However, during a phase change, the heat transfer Q = ±mL, where m is the mass of the object that is going through the phase change, and L is the “heat of fusion” (for a change between liquid and solid), or “heat of vaporization” (for a change between liquid and gas). Q is positive if heat is being added to the object (melting or boiling), or negative if heat is being removed from the object (freezing or condensing). 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 take an ice cube (assumed to start at 0°C), and drop it into a calorimeter cup partially filled with warm water. We will assume that the rest of the calorimeter is perfectly insulating, so that: Qnet = 0, or Qice cube + Qwarm water + 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. However, we must be extremely careful with the Qice cube term: first, the ice cube must melt. Then, the meltwater must itself increase its temperature, until it reaches equilibrium with the original water, and the calorimeter cup. Therefore, a more thorough equation may be: Qice melting + Qmeltwater + Qwarm water + Qcup = 0 Note: if the ice cube had started below 0°C, then we would have had to include a term for the heat required to raise the temperature of the ice to 0°C. [Insert table of heat of fusion, heat of vaporization of water, aluminum] Physics Lab 2 Heat of Fusion PROCEDURE 1. Gather all the necessary materials: triple-beam balance, calorimeter cup, temperature sensor or thermometer, styrofoam cup, and napkins. Note: the temperature sensor that you use in your calorimeter must not have blue plastic tubing at the end. However, never remove the blue plastic tubing from any temperature sensor. 2. Measure the mass of the inner aluminum calorimeter cup only (remove it from the outer cup, and remove the plastic ring) using the triple-beam balance. Note the uncertainty in this mass. 3. At the sink, fill the inner aluminum cup part-way with water. You will want enough to completely melt, 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 ice cube will not melt completely, and you will not be able to get any useful data. How much water to use, and what temperature, is something of a judgment call. If you use too little or too cool, there will be enough time to take another set of data. 4. 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 2. Typical Laboratory Calorimeter Cup (Courtesy of Welch Scientific Co.) 5. 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. 6. Take the ice cube(s) from the container of icewater at the back of the room, and place it in the styrofoam cup. (Since the ice and water have had time to reach equilibrium, it is reasonable to assume that it is at 0°C.) When you get back to your lab bench, dry off the ice as much as possible with the napkin(s). 7. 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. 8. Quickly remove the cover from the calorimeter. Then, drop the ice cube(s) in the inner calorimeter cup, being careful not to splash any water out. Quickly re-cover the calorimeter. (Remember, we want no heat to escape to the outside air.) 9 Gently stir the inner calorimeter cup, until its contents 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 “cool spot,” the equilibrium Physics Lab Heat of Fusion 3 temperature will be near your lowest reading. This is because the calorimeter is not actually a perfect insulator, so the cooler parts will gain heat from the room, desk, etc. as time goes on.) 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.) 10 Remove the inner calorimeter cup, and measure its mass (with the uncertainty). As long as no water spilled or evaporated, the mass of the ice cube (and therefore of the meltwater as well) will simply be this mass, minus the total mass you found in step 4. DO NOT FORGET TO DO THIS STEP! 11. If time allows, you may repeat steps 3-10 for an additional ice cube(s), using a different amount of water at a different initial temperature. Plastic Tubing ANALYSIS 1. Calculate Qwarm water 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 ice cube, calculate the latent heat of fusion of each ice cube. 3. Calculate the % error for each ice cube, using the value in the textbook as the accepted value. measured accepted 100% . Remember: the equation for % error is: %error accepted 4. Using your uncertainties, calculate a worst-case maximum and minimum specific heat for at least one ice cube. 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? Physics Lab Heat of Fusion 4 3. In step 6, if the ice cubes were not dried, and a significant amount of water were accidentally transferred along with the ice as it is placed into the calorimeter, will this result in your calculated heat of fusion being too large or too small? Why? 4. Do the %error results you found surprise you? 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.)