Thermal Equilibrium: The Blacksmith’s Quench

Estimated Time: 45-60 minutes Materials: Computer or tablet with internet access, calculator.

Part 1: Engage (Anchoring Phenomenon)

Imagine a blacksmith shaping a red-hot iron horseshoe. When the shaping is done, the blacksmith plunges the hot iron into a bucket of room-temperature water. A loud hiss is heard, and a cloud of steam rises. If you touch the water a few minutes later, it is noticeably warmer, and the iron is no longer glowing hot—in fact, both the water and the iron are at the exact same temperature.

1. What happens to the thermal energy of the iron and the water when they are combined?
2. Why do the iron and water eventually reach the exact same temperature?

Part 2: Explore (Simulation Investigation)

Open the Thermal Equilibrium Sandbox simulation. This simulation allows you to create a closed system where two materials transfer thermal energy until they reach equilibrium.

Procedure:

1. Set Substance A to Iron.
2. Set the Mass of Substance A to 100 g.
3. Set the Initial Temperature of Substance A to 90 °C.
4. Set Substance B to Water.
5. Set the Mass of Substance B to 200 g.
6. Set the Initial Temperature of Substance B to 20 °C.
7. Click Start Simulation and observe the temperature graph over time.
8. Wait for the system to reach thermal equilibrium (when the temperatures no longer change).
9. Record your data in the table below.

Data Table 1: Iron and Water | Substance | Mass ($m$) | Specific Heat ($c$) | Initial Temp ($T_i$) | Final Temp ($T_f$) | Change in Temp ($\Delta T = T_f - T_i$) | | :— | :— | :— | :— | :— | :— | | Iron | 100 g | 0.45 J/(g·°C) | 90 °C | | | | Water | 200 g | 4.18 J/(g·°C) | 20 °C | | |

Part 3: Explain (Sensemaking)

Thermal energy transfer (heat, $Q$) can be calculated using the equation: \(Q = mc\Delta T\) Where:

• $m$ = mass in grams (g)
• $c$ = specific heat capacity (J/g·°C)
• $\Delta T$ = change in temperature (°C)

1. Calculate the thermal energy transferred ($Q$) for the Iron. (Note: Since the iron cools down, $\Delta T$ will be negative, resulting in a negative $Q$ value, meaning energy was released).
2. Calculate the thermal energy transferred ($Q$) for the Water. (Since the water warms up, $\Delta T$ will be positive, meaning energy was absorbed).
3. Compare the two $Q$ values. How does the amount of thermal energy lost by the iron compare to the thermal energy gained by the water? What does this tell you about the total energy in this closed system?

Part 4: Elaborate / Evaluate (Argumentation & Modeling)

Now, let’s test how different materials affect the final temperature.

1. Press Reset Simulation.
2. Keep Substance B as Water (200 g, 20 °C).
3. Change Substance A to Copper ($c = 0.39$ J/g·°C) but keep its mass at 100 g and initial temperature at 90 °C. Run the simulation and record the final temperature.
4. Press Reset, then change Substance A to Aluminum ($c = 0.90$ J/g·°C) under the same conditions. Run the simulation and record the final temperature.

Argumentation: Construct a scientific explanation to answer the following question:

• How does the transfer of thermal energy between two components at different temperatures lead to a more uniform energy distribution in a closed system?

In your explanation, include:

• Claim: State what happens to the energy of the hot and cold objects until they reach equilibrium.
• Evidence: Use specific numerical data from your investigations (mass, specific heat, initial/final temperatures, and your calculations of $Q$).
• Reasoning: Apply the Second Law of Thermodynamics and the Law of Conservation of Energy to explain why the energy lost by the hot object equals the energy gained by the cold object, and why the final temperature depends on the specific heat capacity ($c$) of the materials.

Teacher Notes & NGSS Alignment

Performance Expectation: 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 (second law of thermodynamics).

Alignment to Dimensions:

• SEP: Planning and Carrying Out Investigations - Students use the simulation to produce data regarding initial and final temperatures, serving as the basis for evidence of energy transfer.
• DCI: PS3.B: Conservation of Energy and Energy Transfer - Uncontrolled systems always evolve toward more stable states—that is, toward more uniform energy distribution (e.g., objects hotter than their surrounding environment cool down).
• CCC: Systems and System Models - When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models.

Evidence Statement Mapping:

• 1.a: Students describe the purpose of the investigation, which includes the idea 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 (second law of thermodynamics). Demonstrated in Part 4 when students construct a scientific explanation about uniform energy distribution.
• 2.a: Students develop a plan and describe the data that will be collected and the evidence to be derived from the data, including the measurement of the reduction of temperature of the hot object and the increase in temperature of the cold object to show that the thermal energy lost by the hot object is equal to the thermal energy gained by the cold object. Demonstrated in Parts 2 and 3 through data collection and $Q = mc\Delta T$ calculations showing equal energy transfer.
• 3.a: In the investigation plan, students describe how a nearly closed system will be constructed, including the boundaries and initial conditions, and the data that will be collected (masses of components and initial and final temperatures). Demonstrated in Part 2 as students explicitly define the system’s materials, masses, and initial conditions before investigating.
• 4.a: Students collect and record data that can be used to calculate the change in thermal energy of each of the two components of the system. Demonstrated in Part 2 and Part 3 where students record temperature changes and calculate $Q$ for each component.