Calorimetry Final Temperature Calculator
When two substances at different temperatures are mixed in an insulated container, heat flows from the hotter to the cooler substance until both reach the same final equilibrium temperature. The principle of conservation of energy states that the heat lost by one substance equals the heat gained by the other, assuming no heat is exchanged with the surroundings. This calculator solves the heat balance equation m1 c1 (T1 - Tf) = m2 c2 (Tf - T2) for the final temperature Tf. It is used in chemistry calorimetry experiments, food science, and industrial mixing calculations.
Calorimetry heat balance formula
Tf = (m1 c1 T1 + m2 c2 T2) / (m1 c1 + m2 c2)
Derived from conservation of energy: heat lost by hotter substance = heat gained by cooler substance. m1 c1 (T1 - Tf) = m2 c2 (Tf - T2). Q = m1 c1 (T1 - Tf).
Worked example
- 100 g of water at 80 degrees C mixed with 200 g of water at 20 degrees C.
- Tf = (100 x 4.184 x 80 + 200 x 4.184 x 20) / (100 x 4.184 + 200 x 4.184)
- Tf = (33,472 + 16,736) / (418.4 + 836.8) = 50,208 / 1,255.2 = 40.00 degrees C
- Q = 100 x 4.184 x (80 - 40) = 16,736 J
Frequently asked questions
What is the calorimetry heat balance equation?
When two substances are mixed and reach thermal equilibrium with no heat lost to surroundings, the heat lost by the hotter substance equals the heat gained by the cooler one: m1 c1 (T1 - Tf) = m2 c2 (Tf - T2). Solving for Tf gives the final temperature.
What is specific heat capacity?
Specific heat capacity (c) is the amount of heat required to raise 1 gram of a substance by 1 Kelvin (or 1 degree C). Water has c = 4.184 J/(g K), iron c = 0.449 J/(g K), aluminum c = 0.900 J/(g K), copper c = 0.385 J/(g K). Values from NIST.
What assumptions does this calculation make?
The calculation assumes a perfectly insulated (adiabatic) system with no heat exchanged with surroundings. No phase changes occur (no melting or boiling). The specific heats are constant over the temperature range.
What units should I use?
Mass in grams (g) or kilograms (kg), specific heat in J/(g K) or J/(kg K) respectively, and temperature in Celsius or Kelvin. Both substances must use the same mass and specific heat units.
What happens if both substances are the same material?
If c1 = c2, the equation simplifies to Tf = (m1 T1 + m2 T2) / (m1 + m2), which is the mass-weighted average temperature.
Official sources
- NIST WebBook: Thermophysical Properties of Fluid Systems.
- NIST: NIST Specific Heat Data.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.