Calorimetry: Mixing Hot and Cold

1 · Predict

A hot aluminium block is dropped into cooler water. If you use a bigger aluminium block (more mass) at the same starting temperature, does the final equilibrium temperature go up or down?

• A bigger hot block raises the final equilibrium temperature.
• A bigger hot block lowers the final equilibrium temperature.
• The final temperature doesn't depend on the aluminium block's mass.

2 · Set Up

1. Open the hot-cold-mix preset and press Reset. 1 kg of water at 290 K (body1) will mix with an aluminium block at 400 K (body2).
2. Enable the equilibrium-temperature readout.
3. Set the aluminium block's mass for each trial and record the equilibrium temperature.

3 · Collect Data

Plot equilibrium temperature T_eq (y-axis) against aluminium mass m₂ (x-axis) for your three trials.

4 · Analyze

1. For one trial, compute T_eq = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂) using water m₁ = 1 kg, c₁ = 4186 J/(kg·K), T₁ = 290 K, and aluminium c₂ = 900 J/(kg·K), T₂ = 400 K. Compare to the table.
2. Explain why increasing the hot block's mass pulls the equilibrium temperature higher, even though its specific heat (900 J/(kg·K)) is much lower than water's (4186 J/(kg·K)).

5 · Extend

1. Water has an unusually high specific heat compared to most materials. Explain why coastal climates tend to have milder temperature swings than inland areas, using the same energy-balance idea as this experiment.
2. The heat lost by the aluminium block should exactly equal the heat gained by the water (energy conservation, assuming no losses to the surroundings). For one trial, verify this using Q = mcΔT for each body.

The Physics Behind This Experiment

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