Thermodynamics
Hot & cold mixing
Mix a hot and a cold body; find the equilibrium temperature.
Hot & cold mixing — interactive Thermodynamics simulation. Mix a hot and a cold body; find the equilibrium temperature. Free browser-based virtual physics lab with live SI measurements and a guided tutorial.
Thermal equilibrium
Mix a hot and a cold body; find the equilibrium temperature.
Calorimetry assumes an isolated system: heat lost by the warm body equals heat gained by the cold one. The final temperature is the mass-weighted average of initial temperatures when specific heats match. This preset uses explicit heat capacities to make the approach to equilibrium visible.
- Q_lost = Q_gained
- T_eq weighted by mc
Investigation brief
Plan the question before you open the lab
The brief mirrors the prerendered page: driving question, competing predictions, variable roles, governing laws, setup, analysis and extension prompts remain visible and in this order.
Driving question
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?
Predictions to weigh
- 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.
Variable roles
What you set:
- Aluminium mass m₂ (kg)
What you measure:
- Equilibrium temperature T_eq (K)
How the investigation runs
- 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).
- Enable the equilibrium-temperature readout.
- Set the aluminium block's mass for each trial and record the equilibrium temperature.
Governing equation
Calorimetric Equilibrium Temperature — T_eq = Σ mᵢcᵢTᵢ / Σ mᵢcᵢ
When two bodies exchange heat with no losses to the surroundings, they settle at a weighted-average temperature — weighted by each body's heat capacity m·c, not just its mass.
What the printable worksheet asks students to work out
- 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.
- 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)).
Where this shows up beyond the lab
- 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.
- 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.
- AP Physics 2 — Unit 9: Thermodynamics
- IB Physics — B.1 Thermal energy transfers
- General High School Physics — Heat, temperature & gas laws
- NGSS High School Physics — Thermal energy transfer
- Middle School Physical Science — Energy transfer between materials
- Welcome to Hot Cold Mix
- Select the cold body
- Press Play
- Mixing to one temperature
- Open the Properties panel
- You did it!
Open the interactive simulation to build the scene, press Play, and explore with live measurements and a guided tutorial.