# Calorimetry Heat Transfer Calculator

> Find the equilibrium temperature when a hot object meets water or another body, and the heat exchanged, with an optional calorimeter heat capacity.

Category: Science & engineering · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/calorimetry-heat-transfer-calculator

In an insulated calorimeter, heat lost by the hot body equals heat gained by the cold one. The final temperature is the heat-capacity-weighted average of the starting temperatures.

Also called: Equilibrium temperature calculator, Mixing temperature calculator.

## Inputs
- Mass of the hot object (unit kg; default 0.5)
- Specific heat of the hot object (unit J/(kg·K); default 897)
- Starting temperature of the hot object (unit °C; default 100)
- Mass of the water (second body) (unit kg; default 1)
- Specific heat of the water (second body) (unit J/(kg·K); default 4184)
- Starting temperature of the water (second body) (unit °C; default 20)
- Calorimeter heat capacity (unit J/K; default ; optional)

## Results
- Final (equilibrium) temperature
- Heat transferred from the hot object
- Temperature change of the hot object
- Temperature change of the water

## Formula

```
T_f = (m₁c₁T₁ + (m₂c₂ + C_cal)T₂) ÷ (m₁c₁ + m₂c₂ + C_cal);  Q = m₁c₁(T₁ − T_f)
```

Where:
- m₁, c₁, T₁: mass, specific heat and starting temperature of the hot object
- m₂, c₂, T₂: the same for the water or second body
- C_cal: heat capacity of the calorimeter cup

## Worked example
1. m₁c₁ = 0.5 × 897 = 448.5 J/K; m₂c₂ = 1 × 4184 = 4184 J/K.
2. T_f = (448.5 × 100 + 4184 × 20) ÷ (448.5 + 4184) = 128 530 ÷ 4632.5 = 27.745 °C.
3. Q = 448.5 × (100 − 27.745) = 32 406 J = 32.41 kJ.

**Result:** A 0.5 kg block of aluminium at 100 °C dropped into 1 kg of water at 20 °C brings both to about 27.7 °C, transferring 32.4 kJ.

## What the result means

Water’s large specific heat means it changes temperature much less than the metal. Measure T_f in the lab and you can solve the same balance backwards for an unknown specific heat.

## Assumptions and limits
- The system is insulated: no heat is lost to the surroundings.
- No phase change or chemical reaction occurs.
- Specific heats are constant.
- If the result is above 100 °C or below 0 °C for water, a phase change would occur and this result is not valid.

## Questions

### What is the calorimeter constant?

The heat capacity of the cup, stirrer and thermometer in J/K. It is found by mixing known masses of hot and cold water and is added to the cold side.

### Why is the heat released positive?

It is measured from the hot object’s point of view: it loses that much energy, and the water gains the same amount.

## Related calculators
- [Heat Capacity Calculator](https://calculators.geekmidst.com/calculators/heat-capacity-calculator)
- [Temperature Converter](https://calculators.geekmidst.com/calculators/temperature-converter)
- [Thermal Expansion Calculator](https://calculators.geekmidst.com/calculators/thermal-expansion-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/calorimetry-heat-transfer-calculator