Mixing Temperature Calculator (Final Temperature of Two Substances)
The temperature two amounts of water, or any two substances, settle at when mixed or put in contact, and the heat that moves between them.
Results
The dashed line marks the value you entered.
What this tool does
When two things at different temperatures meet and nothing escapes to the surroundings, the heat one loses is exactly the heat the other gains, which gives T = (m₁c₁T₁ + m₂c₂T₂) ÷ (m₁c₁ + m₂c₂): an average weighted by heat capacity m × c. Water's specific heat is large — about 4186 J/(kg·K) against about 900 for aluminium and about 385 for copper — which is why a hot piece of metal barely warms a bucket of water. The result holds only if nothing melts, freezes or boils on the way (melting ice absorbs about 334 kJ/kg at 0 °C) and ignores heat lost to the container and the air.
Formula
T_final = (m₁ c₁ T₁ + m₂ c₂ T₂) ÷ (m₁ c₁ + m₂ c₂)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
m1 | Mass of the first substance | kg |
c1 | Specific heat of the first substance (water 4186) | J/(kg·K) |
t1 | First temperature | °C |
m2 | Mass of the second substance | kg |
c2 | Specific heat of the second substance (water 4186) | J/(kg·K) |
t2 | Second temperature | °C |
TF | Final temperature of the mixture | °C |
Q | Heat passed from the hotter to the colder | kJ |
D1 | Temperature change of the first substance | °C |
D2 | Temperature change of the second substance | °C |
Worked example
- Mass of the first substance2 kg
- Specific heat of the first substance (water 4186)4186 J/(kg·K)
- First temperature80 °C
- Mass of the second substance3 kg
- Specific heat of the second substance (water 4186)4186 J/(kg·K)
- Second temperature20 °C
- Final temperature of the mixture44.00 °C
- Heat passed from the hotter to the colder301.39 kJ
- Temperature change of the first substance-36.00 °C
- Temperature change of the second substance24.00 °C
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.