IDS 102 Winter 2011 Heat and Temperature, Part IV Specific Heat and the Importance of Water The weather pattern around Puget Sound, in the region west of the Cascade Mountains, is very different from the weather patterns around Yakima, east of the Cascades. In a normal year, where would you expect to see the highest temperatures: east or west of the Cascades? In a normal year, where would you expect to see the lowest temperatures: east or west of the Cascades? There are lots of factors that combine to produce the differences noted above, but the biggest one has to do with something that seems to be all around us when we are west of the Cascades. It isn't completely absent east of the Cascades but there is a lot less of it. Take a guess. It's... Your answer above may or may not be correct, but try to think of a reason or a few reasons (this is a prediction, so it may also be completely incorrect) why the presence of this stuff would have this influence on temperatures around here. Discuss your ideas with your classmates. Did your explanation have anything to do with the tremendous sizes of some bodies of water around here? If so, good job! Imagine a week in Chicago (next to Lake Michigan) where it has been 10 o C for the entire week. Even in these conditions Lake Michigan doesn t freeze. But here s the interesting thing. If you took a thermometer and measured the temperature of both the lake and the surrounding ground (mostly sand), you would find that the ground was colder than the lake. The ground temperature might be as low as 5 o C or even lower! Now here's the strange part: there is more ground in the Chicago area than there is water in Lake Michigan, so the size of the lake alone does not explain this observation. The same thing happens in the summer. It can get to be 38 o C (100 o F) in Chicago in the summer, and even then Lake Michigan will never get warmer than 27 o C (80 o F). Yet the sand, sidewalks, and roads are all roasting hot. Even a small amount of water can stabilize temperatures more than you might think. Farmers will often store a barrel or two of water in the same shed where they store their fruit in winter. In sheds without water barrels the fruit freezes solid (and is often ruined). In sheds with water barrels the fruit stays nice and cold but generally above freezing. Page 1
Think about what you know about heat and its relationship to water temperature. Remember that for water: heat (cal) = mass (g) x T ( C) Now let s think about a material other than water: The soil and rocks around Lake Michigan change temperature more than the water does when receiving the same amount of heat from the sun. Which side of the above equation will increase for soil and rocks? To really answer this question we need to do an experiment about a concept called specific heat. In this experiment we ll be looking at the factors that affect heat transfer between the rock (= a piece of metal for our experiment) and Lake Michigan (= some water in a foam cup). First, think back to a previous experiment where you mixed different amounts of water at different temperatures and measured the final temperature. Refresher Question: If 50 g of water at 0 o C is mixed with 50 g of water at 60 o C, what do you expect will be the final temperature of the water? If 50 g. of water at 0 o C is mixed with 100 g of water at 60 o C, what do you expect will be the final temperature of the water? (an estimate is okay) Hopefully you recall that the amount of heat transferred between two objects depends on two things: the temperature of the objects and the mass of the objects. There s a third factor as well, one that has to do with the material(s) that the objects are made of. In your experiments with the water you didn t observe this effect because you only experimented with one substance (water). Our next experiments introduce this third variable by looking at heat transfer between different substances. Page 2
Now it s time to get started on the experiment. Here s what you ll need. Before starting, assemble the following items at your desk. A partner or small group. You will be assigned to a group. You'll need more than two hands for this experiment! A set of metal cylinders (your group will use only one, assigned by your instructor). Two Styrofoam cups, one with a cover. Enough room temperature water to cover your metal in the foam cup. A scale for measuring the mass of your water and your metal A source of hot water to be used for heating your metal A thermometer A piece of string Experiments often begin with questions, so here s a question: Which substance will have the greater ability to change the temperature of the other object: water or metal? (Guess and discuss with your group members) In order to look at heat transfer, the metal and the water will need to be at different temperatures. We can add cold metal to hot water, or hot metal to cold water. We will use hot metal added to cold water because it is easier. It s important that you measure the mass of the cup here, as you will then need to get the mass of water only later. Record this cup mass somewhere! Get an idea for how much room temperature water is needed to cover your piece of metal in your foam cup... You want to be able to cover the metal and gently swirl the water without exposing the metal to too much air, but not much more than that. Once you have the right amount of water, carefully record the mass of the water only (in the following table) and set it aside. This is your room temp. water. Now, measure and record (in the following table) the mass of your metal. Next we need to heat the metal to a known temperature. The easiest way to do that is to immerse it in hot water (of a known temperature) for a long enough period of time that we can be confident that the hot water and the metal are at the same temperature. Tie a string around the hook on the metal rod, and then hang the metal in some hot water. Let it stay there for a couple of minutes. Record the temperature of the hot water. This will be the initial temperature of metal. Record this number in the table Measure and record the temperature of the room temperature water. (It should be about 20-ish degrees Celsius). This will be the initial temperature of water. Record this number in the table. Page 3
Data Table: When you are ready, quickly remove the metal from the hot water, tap it to remove drops of hot water, and quickly immerse it in the room temperature water in the foam cup. Cover the foam cup and gently swirl the room temp. water around the metal until you think the water and metal no longer change temperatures. Record the final temperature. This will be the final temperature of both your metal and your water. Record in the table. Repeat the experiment two more times. Do your best to match the amount of water and initial water temperature used in your first trial. Record your data below. Mass of metal (g) Mass of Water (g) (room temp water) Initial Temperature of metal ( o C) Initial Temperature of Water ( o C) Final Temperature of both ( o C) Trial 1 Trial 2 Trial 3 Average Value (this shouldn't change) (this shouldn't change) In this experiment, the hot metal gave up heat (in calories) to the cooler water. Which was greater, the heat lost by the metal or the heat absorbed by the water? (Yes, this is a trick question. Explain why.) Which was greater, the change in temperature of the metal or the change in temperature of the water? (This is not a trick question.) Let s calculate the heat and changes in temperature to really see the difference. Recall that we use the symbol Δ to mean change in. For example, ΔT means the change in temperature. Since we sort of understand water, let's focus on the water first- Use your average values Page 4
Initial temp. (T 0 ) water ( C) Final temp. (T f ) water ( C) ΔT water ( C) Mass of water (g) Heat gained by the water (Cal) If this heat was gained by the water, where did it come from? By concentrating on the water, we have learned the amount of heat that was exchanged.. It is now time to focus on the metal. Again, you should use the average values. 1 Heat lost by the metal (cal) 2 Mass of metal (g) 3 Heat lost by each gram of metal (cal/g) The amount that the temperature of water would 4 have changed if each gram had lost the heat shown in 3 above. ( C) 5 Initial temp. of the metal ( C) 6 Final temp of the metal ( C) 7 ΔT metal ( C) 8 The amount of heat lost per gram of water that would produce this same ΔT metal (cal/g) Compare the temperature changes in line 4 and line 7 in the previous table. Which is greater: the temperature change of the metal or the amount that the temperature would have changed had the metal been made of water? Compare the amounts of heat lost in lines 3 and 8 of the previous table. Which is greater: the heat required to get a certain temperature change in water or the heat required to get the same temperature change in your metal? Page 5
Copy rows three and seven from your previous table into this table, and then calculate the new quantity: The amount of heat per gram per degree of temperature change. What would the units be? 3 Heat lost by each gram of metal (cal/g) 7 ΔT metal ( C) New! The amount of heat lost per gram per degree of change in temp. (divide row 3 by row 7) (cal/g C) Copy rows three and eight from your original table into this table, and then calculate the new quantity: The amount of heat required to change the temperature of your metal compared to the amount of heat required to change the temp of water. What would the units be? 3 Heat lost by each gram of metal (cal/g) 8 New! Heat lost per gram of water that would produce this same change in temp. (cal/g) The amount of heat needed to change the temp. of this metal compared to the amount of heat needed to change the temp. of the water (divide row 3 by row 8) You should see that the numbers for the previous two "new" quantities are the same (or close to it). The units and the interpretations are somewhat different but they tell us the same thing, so they are essentially the same quantity. This quantity is called specific heat. Specific Heat The amount of heat energy required to raise (or lower) the temperature of 1 gram of a substance by 1 o C. All substances have different specific heats. The specific heat of water, for example, is 1.0 cal/g o C. This means that it takes one calorie to raise the temperature of 1 gram of water by 1 o C. (Remember that the calorie is a unit for heat or thermal energy). Test your understanding of this concept by answering the questions below. Include units with your answers. Was the specific heat of your metal greater than, or less than, the specific heat of water? Page 6
Your metal probably changed temperature by more than one degree. Would the amount of heat required to change the temperature of your metal by one degree be greater than, or less than, it would have been for the same mass of water? We mentioned that the equation heat (cal) = (mass (g)) X ( T ( C)) only works for water. You may have noticed that even for water the units in the equation do not work out right. In order to make the units work out right, and in order to make the equation apply to things other than water, we need to insert specific heat (abbreviated s), but where? What units are need to be added where to fix the equation below: heat (cal) = X (mass (g)) X ( T ( o C)) Check your answer with an instructor before continuing. The reason that the numbers for the "new" quantities turned out to be the same is that the specific heat of water in these units is just one (cal/g o C). So the specific heat tells us both how much heat is required to change the temperature of a gram of material AND how hard it is to change the temperature of that material compared to water. For this reason, specific heat is sometimes also called the "water equivalent for heat." Almost every substance we encounter has a specific heat which is LESS than the specific heat of water. This is why water changes temperature so little, with a given amount of heat input compared to the change of temperature of other the things around it. Go back to your table. Based on your experiments, try to estimate the specific heat for your metal. There were lots of sources of error in our experiment. There were lots of places for heat to go besides just the metal and the water. Nonetheless, see how you did. Look up the specific heat values of common metals and predict what metal you had: Page 7
Now that you have an accurate value for the specific heat for your metal, answer this question: Our metal is specific heat: How much heat energy would be required to raise the temperature of 125 grams of your metal from a temperature of 21 o C to a temperature of 25 o C? Check your work with an instructor. Page 8
END OF MODULE QUESTIONS 1. A cup with 40 grams of 90 C water is mixed with a cup with 70 grams of water at 10 C. a. Predict the final temperature of the water. Explain your reasoning. b. Calculate the expected final temperature of the water. (Assume that no heat is lost to the surroundings). 2. 10 calories of heat were added to both a sample of water and a sample of copper. a) The 10 calories of heat increased the temperature of a sample of water by 5 C. What was the mass of the water? b) The 10 calories of heat increased the temperature of 22 g of copper by 5 C. Find the specific heat of copper. Page 9
3. In a lab experiment, an 80 g sample of water at 20 o C is mixed with 80 g of aluminum at 50 o C. The specific heat of aluminum is 0.20 cal/g o C. In other words, it takes only 0.2 calories to raise the temperature of 1 g of aluminum by 1 o C. a. What is your estimation of what the final temperature of the mixture will be? (Do not do any calculations yet). Explain your reasoning. b. How many calories are required to change the temperature of 1 gram of aluminum by 5 o C? Show your work. c. How many calories are required to change the temperature of 80 grams of aluminum by 5 o C? Show your work. Page 10
d. Complete the following table by filling in the number of calories needed to change the temperature of the aluminum by 5 o C, and the resulting temperature change of the cold water. Continue until you have determined the final temperature of the mixture. (Note: if you have trouble doing this in 5 o C increments, you can do it in 1 o C increments, but it will take many more steps) Total Calories Transferred Temperature of 80 g of Al 0 50 o C 45 C Temperature of 80 g of cold water 20 o C e. What is the final temperature of the mixture? f. How many total calories are transferred? g. What is the temperature change of the water in this experiment? h. What is the temperature change of the metal in this experiment? g. Compare the heat lost by the metal to the heat gained by the water. Explain your reasoning. Page 11