Mixing Final Temperature Calculator
Find the equilibrium temperature when two substances at different temperatures are mixed, from their masses, specific heats and starting temperatures.
How it works
T_f = ( m₁·c₁·T₁ + m₂·c₂·T₂ ) / ( m₁·c₁ + m₂·c₂ )
When two substances at different temperatures are mixed in an insulated container, heat flows from the hotter to the cooler one until they reach a common temperature. Energy conservation says the heat lost by one equals the heat gained by the other, and solving that balance gives the final temperature as a heat-capacity-weighted average of the two starting temperatures. Substances with larger mass × specific heat pull the result closer to their own temperature.
Worked example
Mix 100 g of water at 80 °C with 100 g of water at 20 °C (c = 4.184 J/g·°C for both): T_f = (100·4.184·80 + 100·4.184·20) / (100·4.184 + 100·4.184) = 50.0 °C, the simple midpoint because the two are identical in mass and specific heat.
Sources: Calorimetry — Wikipedia
Frequently asked questions
Why is the final temperature not always the midpoint?
It is a weighted average by heat capacity (mass × specific heat). If one substance has more mass or a higher specific heat, it resists temperature change more and the equilibrium lands closer to its starting temperature.
Does this assume no heat loss?
Yes — it assumes an ideal, perfectly insulated system where all heat exchanged stays between the two substances. In a real calorimeter some heat leaks to the surroundings, so measured values differ slightly.
Can the two substances be different materials?
Yes. Enter each one’s own mass and specific heat — for example hot metal dropped into water — and the formula handles the mismatch automatically.
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This calculator is for educational purposes. Double-check important results before acting on them.