##
* *Reflection: Staircase of Complexity
Tracking Energy Flow in Heat-Related problems - Section 3: Whole Class Calorimetry Problem Practice

*Practice what is necessary*

*Staircase of Complexity: Practice what is necessary*

# Tracking Energy Flow in Heat-Related problems

Lesson 4 of 5

## Objective: SWBAT define specific heat and identify the direction of energy flow both conceptually and quantitatively using the calorimetry equation.

In the previous lesson, students experimented with the flow of heat between water samples at different temperatures. In the final lesson of this abridged unit, students will experiment with the flow of heat from hot metals into cold water.

Today's lesson explores the qualitative and quantitative aspects of the flow of heat between objects. We finish with particular emphasis on the mathematical relationships within the specific heat equation q=mc(deltaT), first introduced to students on day one of the unit. Students will need a passing familiarity with this equation in order to attempt to identify an unknown metal sample in the coming lab.

Due to the end of the semester time crunch, this became our only day practicing these calculations. Ideally, we would have had more practice and conducted additional lab investigations to expand student understanding of the concept.

This lesson connects to **Science and Engineering Practice 4**, *analyzing and interpreting data*, and **Science and Engineering Practice 5**, *using mathematical and computational thinking*. It also aligns with the **Energy and Matter Cross Cutting Concept**:* Changes of energy and matter in a system can be described in terms of energy and matter flows into, out of, and within that system*. This lesson continues our exploration of **HS-PS3-4**,* plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system. *

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#### Energy Flow Notes

*25 min*

As students enter the class, I return their papers from the previous day's lab on mixing water at different temperatures. We briefly discuss their results, with focus on how the temperature, and therefore the energy, evened out in each mixture.

I then state that we will be taking our final set of notes of the year, which brings much cheering. While students get out their notebooks, I quickly enter attendance and switch to the projection of the Energy Flow notes.

Highlights from the slideshow:

- This discussion of kinetic energy as dependent on mass, something we omitted in our Reaction Rate unit. I discuss how slow, heavier atoms and molecules can have the same energy as much faster, lighter atoms and molecules. I mention how this is a preview of a concept they will see in first semester physics the following year.
- Students always misinterpret the graph on slide 2, which is the lesson image at the top of the page. They assume the highest graph is the fastest, and therefore the hottest. Either one or two students will contradict the class, because they read the X-axis label of "molecular speed" or I prompt the class to read the labels.
- The next three slides back up what they experienced in lab, that heat flows from high energy to low energy, via collisions (mixing) and that the change may not be equal because it is a relationship between the mass, the amount of heat, the identity of the chemical, and difference in temperatures.
- With the next slide, I perform my specific heat analogy for the class, as seen in this video. Some students saw the visual in class in small groups, but this time everyone can see how the smaller the capacity, the less energy it can hold without changing temperature.
- We finish with reviewing the heat equation and looking at a data sample, and discussing the difference between heat flowing into and out of a system.

Most students are still in the habit of copying each slide. Some, like this sample, have begun to understand how crucial the visuals and diagrams are to understanding science and have begun to build them into their notes more.

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I encourage students to keep their notes out, and to grab a highlighter if they want, while I pass out the Calorimetry Problems. This sheet has seven different word problems using the heat equation, where students will solve for various variables.

From our stoichiometry work earlier in the semester, I know students can plug and chug equations in their calculator, so today's focus is on dissecting the problem for the information present, and then setting up the problem correctly. We only worked out the first problem, with the emphasis beyond that being in the setup. For a more detailed explanation of why, please see the reflection attached to this lesson.

I project the worksheet using the document camera and ask students to read and mark the information in the first problem. I give them a minute before asking them for information.

*What is q?***207J***Positive or negative?***Positive***Why?***Because it is added.***What is the mass?***28.4g***What is c, the specific heat capacity?***We don't know, we're solving for it.***What else do they tell us?***Temperature increased 8.1 degrees.***Where does that go?***Delta-T***Do we have an initial or final temperature?***No, because they already calculated delta-T***Now plug everything into the equation and solve for c.*

Students solve the first equation and get an answer of c=.899 I then give them a chance to set up number 2 on their own and we then check it over as a whole class. At this point, I tell them to put their calculators away, as they will use the remaining time to read and set up the remaining problems.

For students who struggle with reading word problems, I have them take four different color highlighters. Each variable gets its own color, so as they read the problem, they highlight what variable it corresponds with. This visual organizer helps them make sense of the problem and organize their information to be ready to complete the mathematics.

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#### Individual Practice

*15 min*

In the remaining time, I circulate the room to answer students questions and monitor their work. Many students are confused by the complex unit of specific heat, and with so little time remaining in the year, I permit them to ignore it so long as they can recognize it.

Most students get the concept right away, and even can extend to differentiating when there is information on two different chemicals as in numbers five through seven. However, these students struggle with putting all of the information correctly into the chart or equation. I prompt them to set up two different equations, one for each chemical.

Knowing that tomorrow's lab will require this level of mathematical complexity, I use this information to adapt the lab paper to make their calculations easier to figure out for the following day.

However, not all students remain focused when I am not standing by their table and do not finish before the bell rings. I collect the paper from all students so that I can assess progress, and mentally note which ones I believe struggled on the concept and which simply lacked focus in the end of the lesson. The key can be found here.

#### Resources

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