# Thermal Equilibrium Calculator

URL: https://speedycalculator.com/calculators/physics/thermal-equilibrium/
Last updated: 2026-10-30

> The thermal equilibrium calculator finds the final temperature when two bodies at different temperatures exchange heat until they reach equilibrium, from their masses and specific heats.

## Inputs

- Body 1 material
- Body 1 specific heat (J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C))
- Body 1 mass (kg, g, mg, t, lb, oz)
- Body 1 temperature (°C, °F, K)
- Body 2 material
- Body 2 specific heat (J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C))
- Body 2 mass (kg, g, mg, t, lb, oz)
- Body 2 temperature (°C, °F, K)

## Results

- Final temperature
- Heat transferred

## Formula

```
T_f = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)
```

## Explanation

Drop a hot metal block into cold water and both end up at the same temperature. Energy conservation gives that final temperature – a classic way to measure specific heats.

### How to use the Thermal Equilibrium Calculator

- **Body 1 material**
- **Body 1 specific heat**
- **Body 1 mass**
- **Body 1 temperature**
- **Body 2 material**
- **Body 2 specific heat**
- **Body 2 mass**
- **Body 2 temperature**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the materials, enter the masses and starting temperatures. Phase changes are not included.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterBody 1 materialChoose one: Water, Ice, Steam, Air …Body 1 specific heatUnits: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C)Body 1 massUnits: kg, g, mg, t, lb, ozBody 1 temperatureUnits: °C, °F, KBody 2 materialChoose one: Water, Ice, Steam, Air …Body 2 specific heatUnits: J/(kg·K), kJ/(kg·K), J/(g·K), BTU/(lb·°F), cal/(g·°C)Body 2 massUnits: kg, g, mg, t, lb, ozBody 2 temperatureUnits: °C, °F, K

### What each result means

- **Final temperature** = ([C1]×[Body 1 temperature] + [C2]×[Body 2 temperature])÷([C1] + [C2])
- **Heat transferred** = abs([C1]×([Body 1 temperature] - ([C1]×[Body 1 temperature] + [C2]×[Body 2 temperature])÷([C1] + [C2])))

### Example values

How the main result changes when **Body 1 specific heat** changes and everything else stays at the example values above:

Body 1 specific heat (J/(kg·K))Final temperature (°C)45027.748667527.748690027.74861,12527.74861,35027.74861,80027.7486

## Worked example

Inputs — Body 1 material: Aluminium; Body 1 mass: 0.5 kg; Body 1 temperature: 100 °C; Body 2 material: Water; Body 2 mass: 1 kg; Body 2 temperature: 20 °C.

Results — **Final temperature = 27.7486 °C**; Heat transferred = 32,404.74247 J.

## Key terms

- **Zeroth law**: Basis for defining temperature.

## FAQ

**What is thermal equilibrium?**
When two bodies in contact reach the same temperature and no net heat flows.

**Why is the final temperature closer to the water's?**
Water has a much larger heat capacity.

**What is the zeroth law of thermodynamics?**
Bodies in equilibrium with a third are in equilibrium with each other.

**What about heat lost to the surroundings?**
Real experiments need insulation or corrections.

**What formula does the Thermal Equilibrium Calculator use?**
T_f = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂).


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)