Tricky Calorimetry: Making Sense of the Real World

1. Tricky Calorimetry: Making Sense of the Real World Anna Karelina, Sahana Murthy, Maria Rosario Ruibal Villasenor and Eugenia Etkina Rutgers University, New Jersey http://paer.rutgers.edu/scientificabilities Supported by NSF DUE-0241078

2. The Rutgers PAER group developed laboratory tasks for introductory physics courses, where students design and perform experiments to solve practical problems. We also developed and validated rubrics that allow students to self-assess their work and researchers to score lab reports reliably. We found that the most common difficulties that student face are evaluating the effects of the assumptions that they make building a model of a situation and evaluating uncertainties in measurements. Consequently students have trouble assessing whether their solution of a particular problem makes sense.

3. Reported Study Physics for the sciences: enrollment 180 Major:science Study participants:131 Sections: 6 Teaching Assistants:3 Data: Student lab reports

4. Experiment1 Prediction and testing • You have a Styrofoam cup, half-filled with hot water, some ice at 0oC, a scale, a thermometer, and paper towels. • Your task is to predict the amount of ice (in grams) that you should add to the cup of hot water in order that the ice and water reach a final temperature that is half the initial temperature of the hot water. • Write the following in your notebook: • a) What idea or relationship will you use to make a prediction? • b) Write a brief outline of your procedure, with a labeled sketch. • c) Construct the mathematical procedure needed to make your prediction. • d) List the assumptions you are making in your procedure. How could these assumptions affect the experimental results? • e) What are the possible sources of experimental uncertainty? Use the weakest link rule to estimate the uncertainty in your prediction. • f) Then try the experiment. Did your experimental outcome match your prediction within experimental uncertainty? If not, can you explain the difference using the assumptions you made? • g) What can you conclude about the applicability of the idea/relationship in a) to this particular situation?

5. Task 1 Tips for experiment design • Mathematical model QWaterCooling= QIceMelting +QIceHeating leads to the equation for calculation of ice mass: • Here we make two assumptions: that there is no heat leak, so the temperature is stable, and that there is no ice melting, so ice mass is constant. • These assumptions lead to systematic uncertainties of temperature δT ≈ 1oC and δmice ≈ 1g (depends on duration of the experiment). These uncertainties are much higher than uncertainties due to the accuracy of equipment. • These systematic uncertainties can be minimized by performing the experiment as fast as possible. Using LogPro helps control the temperature drift. • The temperature of water should be chosen not to be too high (about 40 – 50 oC). Students should take as much water as possible, but they should remember to leave some space for ice.

6. Experiment 2 Application • Design two independent experiments to determine the specific heat of the given object. It is not known what material the object is made of. • You have access to the following equipment: water, Styrofoam container, heater, weighing balance, thermometer and timer. • For each method, write the following in your lab-report: • a) First, come up with as many designs as possible to determine the specific heat. Write a brief outline of each. Then choose the best design. Indicate the criteria that you used. • b) Include a verbal description and a labeled sketch of the design you chose. • c) Construct the mathematical procedure you will use. • d) What physical quantities will you measure? • e) List the assumptions you make in your procedure. How could they affect the result? • f) What are the sources of experimental uncertainty? How would you minimize them? • g) Perform the experiment and record your measurements. Make a table if necessary. • h) Calculate the specific heat, based on your procedure and measurements. • i) After you have done both experiments, compare the two outcomes. Discuss if they are close to each other within your experimental uncertainty. if they results are different, can they be explained by the assumptions you made in your procedure? • j) List any shortcomings in the experiment design and how you would address them.

7. Task 2Tips for experiment design • A possible design is to put an object of a known temperature into hot or cold water and measure the change of water temperature. • Mathematical model Qwater + Qobject=0leads to the equation for heat capacitance of the object: • Here we assume that the system is isolated and no energy is lost. • This assumption can be validated by choosing initial temperature of the object equal to room temperature (one example). This would eliminate the loss of energy of the object during its transfer to water. • Since the specific heat of metal object is much smaller than that of water, the change in water temperature may be very small. This increases dramatically the experimental uncertainty in temperature ∆T/ (Tinitial – Tfinal) . • This uncertainty can be minimized if the volume of water is as small as possible. It yields larger ∆Twater and reasonable temperature uncertainty.

8. Typical Student Difficulties 1. Experimental uncertainties (a) 63% of the students did notevaluate experimental uncertainties in both tasks (could not compare two results). (b) 91% of thestudents made a mistake in theevaluation of the experimental uncertainty in the measurement of the temperature (T/T instead T/(Tfinal-Tinitial) (c) 100% of the students did not try to minimize experimental uncertainty by increasing the temperature difference. 2. Theoretical assumptions (a) 62% of the students did not consider a constant-mass assumption (ice melts quickly) (b) 53% of the students did not consider no energy loss assumption (c) 84% of the students did not check validity of the assumptions

9. Uncertainties Since Tfinal–Tinitial is 0.8oC, the relative temperature uncertainty ∆T/(Tfinal–Tinitial) is about 100% Extremely good results in spite of huge temperature uncertainty Comparing two values without evaluating uncertainty correctly leads to a wrong conclusion

10. Assumptions The student did not take into account that temperature may change by several degrees during the experiment, so the uncertainty is much higher than 0.05oC Wrong evaluation of uncertainties leads to a wrong conclusion The idea that increasing equipment precision always improves the experimental results is rather typical. This happens because students do not take into account the effects of the assumptions they made in the procedure. Students confuse standard and systematic errors

11. Validity of Assumptions By the end of the lab most students understood that their assumptions were wrong. In most cases students arrived at correct conclusions what should be done to minimize uncertainties and to improve results. Unfortunately, students did not have time to repeat the experiment to get better results. This left many of them disappointed and miserable.

12. Student Performance 131 students in sample from 6 sections

13. Student performance in different TA sections • TA1 – 1 section, 20 students • TA2 – 2 sections, 42 students • TA3 – 3 sections, 69 students The percentage of students in different sections who 1. evaluated uncertainties 2. tried to minimize effect of assumptions 3. realized effect of the assumptions on the confidence interval 4. realized that assumptions may be wrong and realized how to improve measurements

14. Different TAs - Different Approaches • Did not correct students’ mistakes • Insisted on planning the experiment thoroughly and considering minimizing effects of assumptions • Insisted on analyzing results and thinking about reasons of discrepancies. About 70% of students tried to minimize effects of assumptions, realized that assumptions may have been invalid and suggested improvements TA1 Students did not have time to think about minimizing effect of assumptions Almost all of the students tried to evaluate uncertainties Students realized that assumptions could have been invalid and suggested experimental improvements Insisted that students followed rubrics’ guidelines and wrote responses to all lab questions according to the guidelines TA2 Students did not evaluate uncertainties. Students did not know how judge results in experiment 2 Few realized that assumptions may have been wrong and suggested some improvements to the experiment. • Did not require evaluating of the uncertainties • Did not require a second method in experiment 2 TA3

15. Evaluating effects of assumptions Evaluating uncertainties Model, assumptions Design of experiment Measurements Comparison of results Judgment Improvements Implications for Instruction • TA training should focus on the importance of following the lab guidelines. • The wording of the lab tasks should emphasize the importance of evaluating the validity of assumptions. • Students should have time to make improvements to the experiment and to repeat the measurements to get satisfactory results. • The lab should be divided into two labs so that students have more time to fulfill these requirements.