Name: Investigation #2 Partner(s): TEMPERATURE VS. HEAT These investigations are designed to help you distinguish between two commonly confused concepts in introductory physics. These two concepts, temperature and heat, are fundamental to the understanding of thermodynamics, the study of thermal energy and its conversion to other forms of energy. In short, temperature describes the hotness or coldness of a body (on some numerical scale) and heat is energy that transfers from one body to another because of a difference in temperature between those two bodies. Part I In describing thermal phenomena, we introduce a new concept: temperature. The original definition of temperature was based on our senses. We can feel whether something is hot or cold. In principle, a temperature scale can be designed by assigning specific numbers to different sensations. A much more reliable way to determine temperature is to use a measuring device called a thermometer. A thermometer is any device that has a physical property that changes with temperature. The most familiar thermometer is the liquid-in-glass thermometer. The physical property that changes with temperature is the volume of the liquid. (The volume of the glass changes too. A properly calibrated glass bulb thermometer will take into account the volume changes in the glass as well as the liquid.) Your group will need the following materials/equipment for this part: 2 thermometers ( 1glass bulb and 1 handheld digital) 1 Styrofoam cup Crushed ice Access to boiling water Procedure Using both the glass bulb thermometer and the digital thermometer, measure the temperature of the air, body temperature (inside the elbow) ice water, room temperature water and boiling water. After the thermometers stop changing, record the temperatures in Table 1 below. Table 1 Thermometer Air Temp Body Temp. Room Temp. Water Melting Ice Boiling Water Glass Bulb Hand Held Digital 25
Question: Do both of the thermometers give exactly the same readings? If not, why might they not? Question: Any of these temperatures could be used as a fixed point to define a temperature scale. Which two the above temperatures (not thermometers!) generally do not change over time and therefore are the best choices for defining a reliable scale? Checkpoint: Consult with your instructor before proceeding. Instructor s OK: Part II and Heat Up to this point, you have been exploring the concept of temperature. That is, how hot or cold something is. In this part we introduce the concept of heat. As noted briefly in your predictions, you may already recognize that there is a difference between temperature and heat. The relationship between temperature and heat can be illustrated with an analogy: Suppose that four people having no money are in a room. Suppose that a fifth individual having twenty single dollar bills enters the room. Being a generous person, the person with the $20 decides to distribute the money evenly among everyone now in the room including himself. (That is, the number of people in the room includes the donor.) Questions: Complete Table 2 below and Table 3 on the next page. Table 2 With the 5 people in the room and the donor has initially having $20 How much money did the generous donor give away? $ With the 5 people in the room and the donor has initially having $40 How much money did the generous donor give away? $ 26
Table 3 If instead, 10 people are in the room and the donor evenly distributes $20 How much money did the generous donor give away? $ With 10 people in the room and the donor evenly distributing $40 How much money did the generous donor give away? $ In this analogy, temperature relates to the amount of money that each person has and heat refers to the amount of money that transfers in order to evenly distribute the money. The individuals initially without money are cold and the generous donor is initially hot. After mixing, the individuals achieve thermal equilibrium by equalizing dollars. The total amount of money in the room refers to the internal energy in the combined system. Comment: It should be noted that in a thermodynamic system, the internal energy is the total sum of all the energy associated with the random disordered motion of all the particles in the system. In our money analogy, the amount of money that each individual has more accurately refers to the average kinetic energy per particle in the system. It is important to note that temperature is not the same thing as energy. However, temperature is proportional to the average kinetic energy per molecule so the analogy is still valid. As a final scenario, suppose that there are two donors among all the people in the room. Complete Table 4 below. Table 4 With 5 people in the room and the 2 donors each initially having $20 How much money (total) did the generous donors give away? $ With 10 people in the room and the 2 donors each initially having $40 How much money (total) did the generous donors give away? $ Question: Following the analogy, to what variable does the number of cold individuals and the number of hot individuals correspond in a thermodynamic system? 27
Note: For the following experiments, it is important that you perform your measurements as accurately as possible in order to make sense of your results. For example, use the electronic balance to measure masses, use the graduated cylinder and the dropper to measure the amounts of water needed (being sure to read the graduated cylinder at eye level on a flat stable surface), waiting for the thermometer to stabilize, measuring the mass to the nearest 0.1 g, etc. Your group will need for the following materials/equipment for this part: 1 computer with LoggerPro software installed 1 universal laboratory interface (ULI) box and appropriate cabling 1 stainless steel temperature probe 1 heat pulse controller with immersion heater 1 graduated cylinder with dropper 1 Styrofoam cup 1 metal can (to hold the Styrofoam cup) Water Safety glasses Procedure 1. Connect the temperature probe to CHANNEL 1 of the interface box. 2. Connect the immersion to the heat pulse controller and then connect the controller to channel DIG/SONIC1 of the interface box. You will also have to plug the controller (NOT the immersion heater!) into a standard 120 V outlet. 3. Start the temperature analysis program on the computer by opening the Conceptual Physics folder on the computer desktop. 4. Open the file and Heat in that folder. When the file opens, a Page Information window should appear. Click OK. (A sensor confirmation window may appear. If so, it should indicate the temperature probe in connected to CHANNEL 1 and that the heat pulse controller is connected to DIG/SONIC1. If this is the case, click OK. ) A graph of vs. Time should appear. 5. The Collect button at the top of the screen should turn green indicating that the computer is ready to collect data. Otherwise, inform your instructor if there are persistent problems. Caution: You must NOT activate the heat pulse controller unless the coil of the immersion heater is immersed in the water. Otherwise, you will burn out the heater! 6. Place the Styrofoam cup into the metal can to avoid spillage. 7. Look at the side of the immersion heater and record the power rating (wattage) below: P = W 8. With a graduated cylinder and dropper, measure 60.0 ml of water into the Styrofoam cup. 28
9. Place the temperature probe and the immersion heater into the water. Be sure that the coil of the immersion heater is fully submerged as shown in Fig. 1. Caution: To avoid the risk of an electrical shock, DO NOT immerse the body or cord of the immersion heater as shown in Fig. 1 below. Immersion Heater Probe Caution: Do NOT immerse heater beyond this point! Caution: Be sure that coil of heater is submerged! Fig. 1: Experimental set-up with temperature probe and immersion heater. 10. In the menu bar, go to Experiment, drag down to Set Up Sensors, and select Show All Interfaces. Click on the heat pulse controller interface and be sure that the heat pulser is set for 2 second duration. Then click Close. 11. The temperature probe should be showing a live reading in the upper left corner of the screen. Record the initial temperature in the first row of Table 3 on the next page. 12. Use the temperature probe to gently stir the water. 13. Start the data collection. While the data is recording, click the Pulse button (next to the Collect button). The red light on the heat pulse controller should light for 2.0 s and a marker will appear on the screen indicating that you activated the heater. 14. Continue stirring and pulse the heater four more times in regular time intervals (waiting for each pulse to end before starting the next pulse) for a total of 5 pulses. 15. After the last pulse, keep stirring and allow the collection to continue until the temperature of the water reaches a maximum and start to drop. 16. Have your instructor verify the results of your graph before continuing. Upon instructor approval, print the graph you just acquired. Question: On the instructor-approved printout, draw two vertical lines on the graph to identify following two times: 1) the time you took the initial temperature and 2) the time you took the final (maximum) temperature. Checkpoint: Consult with your instructor before proceeding. Instructor s OK: 29
17. Record the final (maximum) temperature and the change in temperature of the water in Table 3. 18. Perform two more trials by repeating Steps 8-15 using 10 pulses and 20 pulses. Complete Table 3. Table 3 Trial Amount of Water (ml) Number of pulses Initial Water T i Final Water T f Change in T = T f T i (C ) 1 60 5 2 60 10 3 60 20 19. Repeat Steps 8-17 using 120.0 ml and for 180.0 ml of water. Complete Tables 4 and 5 below. Table 4 Trial Amount of Water (ml) Number of pulses Initial Water T i Final Water T f Change in T = T f T i (C ) 1 120 5 2 120 10 3 120 20 Table 5 Trial Amount of Water (ml) Number of pulses Initial Water T i Final Water T f Change in T = T f T i (C ) 1 180 5 2 180 10 3 180 20 30
Questions: How did the change in temperature depend on the number of pulses made in this experiment? Are your results what you expected? Why or why not? Questions: In Tables 3-5, you doubled the amount of heat added to the water in Trial 2 in comparison to Trial 1. By what factor was the change in temperature different in Trial 2 compared to Trial 1 in each experiment? Are these results what you expected? Why or why not? Questions: In Tables 3-5 you doubled the amount of heat added to the water in Trial 3 in comparison to Trial 2. By what factor was the change in temperature different in Trial 3 compared to Trial 2? Are these results what you expected? Why or why not? Questions: In Table 4, you used twice the amount of water than you did in Table 3 for each trial. By what factor was the change in temperature different for each trial in Table 4 compared to each respective trial in Table 3? Are these results what you expected? Why or why not? Questions: In Table 5, you used three times the amount of water than you did in Table 3 for each trial. By what factor was the change in temperature different for each trial in Table 5 compared to each respective trial in Table 3? Are these results what you expected? Why or why not? 31
Question: Based on your results, what seems to be the mathematical relationship between the amount of heat added to a fixed amount substance and the change in temperature of that substance? (Be specific!) Question: Based on your results, what seems to be the mathematical relationship between is the amount of substance and the change in temperature of that substance when a fixed amount of heat is added? (Be specific!) Question: If the duration of each pulse is set for 2 s, use the power rating of the to determine the amount of energy transferred to the water each time the heater is triggered. (Recall that power is the rate at which energy is transferred. That is, P = E/ t.) E = P t = Heat Added per Pulse = J/pulse Question: Do you think that all of the energy per pulse that you calculated above goes completely into the water? Why or why not? Question: You will need the result for the Heat added per Pulse as well as the T information from one of Tables 3-5 in the next laboratory investigation. Choose the table that appears to give the most consistent results. (Check with your instructor if you are not sure.) Be sure to record these results in the table for Homework Question 8 of Investigation #3 on p. 57. Checkpoint: Consult with your instructor before proceeding. Instructor s OK: 32
Part III Water Mixtures In this activity, you will mix different amounts of hot and cold water and observe how the final temperature of the mixture depends on the relative amounts of the hot and cold water. It is helpful to make sure that the there is a significant temperature difference between the hot and cold water. (A 40-50 C temperature difference between the hot and cold water should give fairly clear results.) Your group will need the following materials/equipment for this part: 2 Styrofoam cups with lids hot and cold water (with at least a 40-50 C temperature difference) handheld digital thermometer graduated cylinder and dropper safety goggles Procedure 1. Using a graduated cylinder, measure out the amounts of hot and cold water, as listed in the first row of Table 6 on the next page. Pour them into separate Styrofoam cups and cover the cups with the lids. Measure the initial temperatures of the hot and cold water. NOTE: It is very important that you accurately measure the initial temperatures immediately before you combine the water in order to obtain clear results. 2. After measuring the initial temperature of the water in each cup, carefully (so as not to splash any of the water out of either cup), pour the cold water into the hot water and then pour the mixture back into the first cup. (This helps to ensure good mixing of the water.) 3. Immediately cover the cup containing the mixture and use the thermometer to further stir the water. After allowing the system to stabilize, record the final temperature and complete the first row of Table 6 on the next page. 4. Perform at least four more trials following Steps 1-3 for the amounts of hot and cold water in each of the remaining rows of the table below. Record your results and complete Table 6 below. Question: Noting that 1 ml = 1 cm 3, what is the numerical relationship between the gram mass and the milliliter volume of a given sample of fresh water? (In other words, what is the density of water?) 33
Table 6 Volume of Hot Water V H (ml) Initial Hot Water Temp. T Hi Volume of Cold Water V C (ml) 20.0 100.0 40.0 80.0 60.0 60.0 80.0 40.0 100.0 20.0 Initial Cold Water Temp. T Ci Final Temp. of Mixture T f 5. Using the density of water and volumes recorded in Table 6, enter the masses of the hot and cold water in Table 7 below. 6. Using the initial temperatures from Table 6, complete the remainder of Table 7. Table 7 Mass of Hot Water m H (g) Mass of Cold Water m C (g) Ratio * of Masses of Cold Water to Hot Water m C /m H Change in Temp. of Cold Water T C (C ) Change in Temp. of Hot Water T H (C ) Ratio * of Changes of Hot Water to Cold Water T H / T C * Write your ratios in decimal form (for example 1:5 = 0.20 and 5:1 = 5.0) Question: Based on your data in Table 7, by what multiplicative factor do the ratios of m C /m H and T H / T C appear to be related? Checkout: Consult with your instructor before exiting the lab. Instructor s OK: 34