Final Temperature of Mixing Calculator
Find the equilibrium temperature when two substances at different temperatures are mixed, using mass and specific heat.
How it works
T_f = (m₁·c₁·T₁ + m₂·c₂·T₂) / (m₁·c₁ + m₂·c₂)
When two substances at different temperatures touch, heat flows from hot to cold until both reach one final temperature. Assuming no heat is lost to the surroundings and nothing changes phase, the heat lost by the hotter body equals the heat gained by the cooler one. Solving that balance gives a weighted average of the starting temperatures, weighted by each substance's heat capacity (mass × specific heat).
Worked example
Mix 100 g of water at 80 °C with 100 g of water at 20 °C (c = 4.18 for both): T_f = (100·4.18·80 + 100·4.18·20) / (100·4.18 + 100·4.18) = 50 °C.
Sources: Calorimetry — Wikipedia
Frequently asked questions
Why is the answer a weighted average?
Each substance resists temperature change in proportion to its mass times specific heat. The body with the larger heat capacity pulls the final temperature closer to its own starting value.
Does this account for heat lost to the cup or air?
No — it assumes a perfectly insulated system and no phase change. Real experiments lose some heat, so the measured final temperature is usually slightly different.
What if the substances have different specific heats?
Enter each one's specific heat. Metals, for example, have far lower specific heats than water, so a hot metal barely warms a large mass of water.
Related calculators
Educational estimate. Confirm the balanced equation, units and conditions for your exact problem.