## solutions to warmup - Section 2: Explanation

# Determining Heater Ratings Experimentally - Day 1

Lesson 3 of 14

## Objective: Students will use the techniques developed over the past two days to empirically determine the power rating of immersion heaters.

#### Warm-up

*15 min*

This warm-up provides students with a straightforward problem and a challenge problem (warm-up with extension resource). The straightforward problem reinforces the previous day's lesson. The challenge is to think about the idea that our model assumes that all of the energy from the heaters goes into the sample of water. Clearly, this is not true . . . but how should we adjust our model?

The goal is to recognize that our idealized assumption, while helpful, is likely not accurate. I allow students 5-10 minutes to address the warm-up questions, depending upon the overall depth of engagement. In the ensuing discussion, I promote the idea that the water and the vessel are 'thermally connected' and will, we assume, start and end at the same temperature when subjected to heating. The energy will be distributed, in some way, between the vessel and the water. The nature and extent of that distribution is the topic of the next section.

Additionally, this conversation leads to the problem of energy that flows into the surrounding air. I postpone the consideration of a solution for this until a later time.

#### Resources

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#### Explanation

*10 min*

Students receive a 1-page summary (Energy-Temperature Notes, Part Two resource) of an approach that can be used to examine multiple materials being heated simultaneously. After reading, I lead a short discussion to clarify understanding of the notes. Then I return to the second part of the warmup problem (see solutions to warmup) to demonstrate how we can include the impact of a vessel (beaker, cup, jar, etc.) on our calculations.

I am trying to build enough understanding so that students can experimentally determine the power rating of immersion heaters. Ultimately, I want students to understand that, if they can get a very linear thermal response and measure the slope of that response, they can successfully determine the power rating of their immersion heaters.

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#### Guided Practice

*15 min*

Students then attempt questions 6, 7, 8, and 9 on the previous day's handout (Energy-Temperature Questions). Again, students are encouraged to help one another as they work through these problems.

It is essential that each student tries #9 in that it sets up the lab work for the next two days. If I identify individual students who may be lagging, I ask them to skip ahead to #9.

The purpose in this segment is to preview the kind of problem-solving that will be necessary for successful completion of the lab work.

#### Resources

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#### Prompt for Lab Work

*10 min*

I provide students with a handout (immersion heater lab prompt) to record the "best practices" we developed in the first few days of this unit (stirring the water, fixing the distance between heaters and temperature probes, etc.). After just a minute or so of private thinking and writing, I lead a short discussion to ensure that all students are thinking about these best practices.

I intentionally leave the lab procedure open so that students must decide, for themselves, the most appropriate way to proceed. While this may take some time and may create some false starts, I feel it is a good trade-off: students are making authentic science choices, not just following a recipe. The value of this is, in my estimation, worth the extra time.

Before beginning the data collection phase, I ask students to consider two fictionalized sample data sets. One set is very scattered while the other is very consistent. We discuss the level of confidence one would have in either of the data sets . . . this provides motivation for repeating trials: only with repetition can we know the extent to which our methods are reliable!

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#### Data Collection

*30 min*

Working in randomized teams of 3-4, students begin to collect data to answer the prompt.

This is the first of two days that I allow for this investigation. I find that there is often the need for re-familiarization with the materials, software, analysis, etc. In addition, student groups need time to determine their own process, a valuable but sometimes slow process. I assure students that we will take some time in the next class to continue this process. I circulate among the groups to check in about approaches, procedures, best practices, etc.

Ultimately, what students should be generating are multiple graphs of temperature versus time, under a variety of conditions. These temperature responses should be linear and the slopes can be used to determine the power rating of the immersion heaters.

Some teams will correctly note that there is an inevitable impact of "losses" (to the beakers, to the air). I will discuss this only with those groups that bring it up. The next lesson will make those questions more universally applicable - we'll explore the assumption that all of the heater energy goes into the water.

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- LESSON 1: Introduction to Physics via Thermodynamics
- LESSON 2: Temperature Slopes and Meaning-Making
- LESSON 3: Determining Heater Ratings Experimentally - Day 1
- LESSON 4: Determining Heater Ratings Experimentally - Day 2
- LESSON 5: Wrapping Up the Immersion Heater Investigation
- LESSON 6: Exploring Calorimetry
- LESSON 7: Conservation of Energy . . . To the Rescue!
- LESSON 8: Enhancing Our Energy Model: From Naive to Sophisticated
- LESSON 9: Testing Our Thermal Loss Procedures
- LESSON 10: Hot Rocks Lab Work - Day 1
- LESSON 11: Hot Rocks Lab Work - Day 2
- LESSON 12: Hot Rocks Lab Work - Day 3
- LESSON 13: Kinetic Theory of Matter
- LESSON 14: Reflecting on Thermodynamics - Content and Process