Final temperature of a mixture calculator
Enter the mass, specific heat and temperature of each substance to get the shared temperature at equilibrium. Suited to calorimetry and mixing hot and cold water.
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How to use it
- Enter mass of substance 1, specific heat of substance 1, temperature of substance 1, mass of substance 2, specific heat of substance 2 and temperature of substance 2.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
T = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂), and the heat transferred is Q = m₁c₁ × (T₁ − T).
Example
Inputs: Mass of substance 1 = 1 kg, Specific heat of substance 1 = 4,184 J/(kg·K), Temperature of substance 1 = 80 °C, Mass of substance 2 = 2 kg, Specific heat of substance 2 = 4,184 J/(kg·K). Result: Final temperature: 40 °C; Heat lost by substance 1: 167,360 J.
Limits and caveats
- It assumes an isolated system with no heat lost to the container or the air.
- It does not apply if a phase change such as melting ice or boiling happens during mixing.
Questions about this tool
How do I mix hot and cold water?
Enter 4184 as the specific heat for both, and the result becomes a mass-weighted average.
Can I use liters instead of kilograms for water?
Approximately, yes. A liter of water has a mass close to 1 kg at ordinary temperatures.
Why does a hot metal piece cool so fast in water?
Water has a high specific heat, so it absorbs a lot of heat with only a small rise in temperature.