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Mixing Temperature Calculator

This mixing temperature calculator finds the common final temperature of two quantities, even of different materials, using Richmann’s mixing rule. Example: 2 kg of water at 80 °C and 3 kg of water at 20 °C end up at 44 °C.

Example: What do you want to know: Final temperature of a mixture · Mass of body 1 2 kg · Temperature of body 1 80 °C · Material of body 1: Water (c = 4.182) · Mass of body 2 3 kg · Temperature of body 2 20 °C · Material of body 2: Water (c = 4.182) → Result: Mixing temperature: 44 °C. Source: Wikipedia – Richmannsche Mischungsregel. Updated: .

kg
°C
c = specific heat capacity in kJ/(kg·K), typical values near 20 °C.
kg
°C
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Result

Result
Mixing temperature: 44 °C
Heat capacity and temperature change
BodyHeat capacity m·cTemperature before → after
1 · Water8.364 kJ/K80 → 44 °C (−36 K)
2 · Water12.546 kJ/K20 → 44 °C (+24 K)
Heat transferred301.1 kJ0.08364 kWh
Steps
  • Heat capacities: body 1: 2 kg · 4.182 kJ/(kg·K) = 8.364 kJ/K; body 2: 3 kg · 4.182 kJ/(kg·K) = 12.546 kJ/K.
  • Richmann’s rule: Tm = (k₁·T₁ + k₂·T₂) / (k₁ + k₂) = (8.364·80 + 12.546·20) / (8.364 + 12.546) = 44 °C.
  • The warmer body 1 gives 301.1 kJ to body 2.
The calculation assumes no heat loss to the surroundings and no change of state (melting, boiling). Heat capacities are typical values near 20 °C.

How it is calculated

When two bodies of different temperature are mixed, their temperatures even out: the warmer one gives off exactly as much heat as the colder one takes up. That leads to Richmann’s mixing rule, which gives the common final temperature.

The formula

Each body has a heat capacity k = m·c, mass times specific heat capacity. The mixing temperature is T = (k₁·T₁ + k₂·T₂) / (k₁ + k₂), a weighted average. For the same material c cancels out: 2 kg of water at 80 °C and 3 kg at 20 °C give (2·80 + 3·20) / 5 = 44 °C. Different materials count differently: water with c = 4.182 kJ/(kg·K) stores far more heat than copper with 0.382, so a hot piece of metal barely warms the water it is dropped into. The heat transferred is Q = k·ΔT.

Mixing bath water

In the second mode you set the total amount and the target temperature. For 150 l at 38 °C from 60 °C hot and 15 °C cold water you need 150·(38 − 15) / (60 − 15) ≈ 76.7 l hot and 73.3 l cold.

Frequently asked questions

How do you calculate the mixing temperature?

With T = (m₁·c₁·T₁ + m₂·c₂·T₂) / (m₁·c₁ + m₂·c₂). For two amounts of the same material it is simply the mass-weighted average of the temperatures.

What is specific heat capacity?

It tells you how much heat one kilogram of a material needs to warm by one kelvin. For water it is 4.182 kJ/(kg·K), for iron about 0.45.

How much hot water do I need for a bath?

The hot amount is total amount times (target − cold) divided by (hot − cold). Fill the rest with cold water.

Sources and legal basis

As of: · Editorial policy

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