Unit 3 - Worksheet 1 - Free Printable

You're looking at Unit 3 - Worksheet 1 from Modeling Instruction (AMTA 2012), which asks you to analyze energy changes in three physical situations using energy bar charts (also called LOL diagrams — for “Loss, Gain, or Transfer” of energy). The goal is to represent how thermal energy (E_th), phase/chemical potential energy (E_ph), and chemical energy (E_ch) change from initial to final states, and to describe how particle motion and arrangement change.

Let’s solve each problem step by step.

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## 🔹 Problem 1: A cup of hot coffee cools as it sits on the table.

📊 Energy Bar Chart Analysis:

- Initial State: Coffee is hot → high thermal energy (E_th).
- Final State: Coffee is cooler → lower E_th.
- Energy Flow (Q): Arrow points OUT of the system (coffee) → heat flows from coffee to surroundings.
- E_ph and E_ch: No phase change or chemical reaction → remain unchanged.

✔ So, in the “Final” bar chart:
- E_th bar is shorter than initial.
- E_ph and E_ch bars are same height.

🧠 Particle Motion & Arrangement Explanation:

> As the coffee cools, the average kinetic energy of its particles decreases. This means the particles move more slowly. The arrangement of particles doesn’t change significantly since it remains liquid — no phase change — so intermolecular distances stay roughly the same, but motion becomes less vigorous.

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## 🔹 Problem 2: A can of cold soda warms as it is left on the counter.

📊 Energy Bar Chart Analysis:

- Initial State: Soda is cold → low E_th.
- Final State: Soda is warmer → higher E_th.
- Energy Flow (Q): Arrow points INTO the system (soda) → heat flows from surroundings into soda.
- E_ph and E_ch: No phase change or chemical reaction → unchanged.

✔ In the “Final” bar chart:
- E_th bar is taller than initial.
- E_ph and E_ch bars are same height.

🧠 Particle Motion & Arrangement Explanation:

> As the soda warms, the average kinetic energy of its particles increases. This means the particles move faster. Again, no phase change occurs (still liquid), so particle arrangement remains similar — molecules are still close together but jostle more vigorously.

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## 🔹 Problem 3: A tray of water (20°C) is placed in the freezer and turns into ice cubes (-8°C)

📊 Energy Bar Chart Analysis:

This one is more complex because there’s a phase change (liquid → solid).

- Initial State: Liquid water at 20°C → moderate E_th, some E_ph (potential energy due to molecular spacing in liquid).
- Final State: Ice at -8°C → lower E_th (colder), lower E_ph (solid has less potential energy than liquid — molecules are locked in place).
- Energy Flow (Q): Arrow points OUT of the system → heat is removed from water to freeze it and cool it further.
- E_ch: No chemical reaction → unchanged.

✔ In the “Final” bar chart:
- E_th bar is much shorter (cooled from 20°C to -8°C).
- E_ph bar is shorter than initial (freezing releases latent heat → potential energy decreases).
- E_ch unchanged.

> ⚠️ Note: Even though the water cools *and* freezes, both processes involve loss of energy. Freezing releases energy (latent heat of fusion), so E_ph drops. Cooling lowers E_th.

🧠 Particle Motion & Arrangement Explanation:

> Initially, water molecules are moving relatively freely in the liquid state — sliding past each other with moderate speed. As it cools and freezes, the molecules slow down and settle into a fixed, ordered crystalline structure (ice). Their motion becomes vibrational only (not translational), and their arrangement becomes highly ordered with fixed positions. This reduction in freedom of motion corresponds to decreased thermal energy, and the formation of rigid bonds corresponds to decreased potential energy (E_ph).

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## ✔ Summary Table for Quick Reference:

| Situation | E_th Change | E_ph Change | Q Direction | Particle Motion Change | Particle Arrangement Change |
|------------------------------|-------------------|--------------------|-----------|-------------------------------------|-----------------------------------------|
| Hot coffee cools | Decreases | No change | Out | Slows down | No significant change (still liquid) |
| Cold soda warms | Increases | No change | In | Speeds up | No significant change (still liquid) |
| Water → Ice (-8°C) | Decreases | Decreases (phase) | Out | Slows down → vibrational only | Becomes ordered, rigid crystal lattice |

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## 💡 Final Tips:

- Always ask: Is there a temperature change? → affects E_th.
- Is there a phase change? → affects E_ph.
- Is there a chemical reaction? → affects E_ch.
- Arrows for Q show direction of heat flow: into system = +Q, out of system = -Q.

You’ve now completed the worksheet! You can fill in the bar charts accordingly and write the explanations based on the above.

Let me know if you’d like a visual sketch of the corrected bar charts!