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Calorimetry calculator

Q = mcΔT, latent heat and equilibrium temperature of a mixture, with the sign convention.

Parameters

Body 1
Liquid water: ≈ 4184 J/(kg·K); the real value varies by about ±1% between 0 and 100 °C.
Body 2
All temperatures in the same unit, °C or K; ΔT has the same value in both.

Result

Equilibrium temperature

74.94

Calculation
Teq = (m₁c₁T₁ + m₂c₂T₂) ÷ (m₁c₁ + m₂c₂) = 74.94
Heat capacities
body 1: m·c = 4184 J/K; body 2: m·c = 385 J/K
204060024temperaturekJ/Kbody 1body 274.9
Heat received by body 1−21 150 J
Note

Equilibrium settles at 74.94, between 20 and 80, closer to the body with the larger heat capacity m·c.

Calculation, assumptions and sources

OverviewThree calorimetry calculations: the heat to warm or cool a mass (Q = m·c·ΔT, received or released), the energy of a change of state (Q = m·L) and the equilibrium temperature of a mixture of two bodies.

Three calorimetry calculations: the heat to warm or cool a mass (Q = m·c·ΔT, received or released), the energy of a change of state (Q = m·L) and the equilibrium temperature of a mixture of two bodies. Results are also given in kJ and Wh.

Method & formulasQ = m·c·(T₂ − T₁)
Q = m·c·(T₂ − T₁)Q = m·LTeq = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)

At equilibrium, the heat released by the hot body equals the heat received by the cold one (isolated system).

Sign convention
energy received by the body if Q > 0 (it warms or melts), released if Q < 0 (it cools). The sign comes from ΔT.
Specific heat capacity (c)
the energy needed to raise 1 kg of the body by 1 K, in J/(kg·K). The usual value for water, ≈ 4184, comes from the thermochemical calorie, equal to 4.184 J by definition.
Latent heat (L)
the energy of the change of state per kilogram, at constant temperature (melting or boiling plateau).
Validity domainThe calculation assumes an isolated system, with no loss to the container or the air, and heat capacities constant over the interval.

The calculation assumes an isolated system, with no loss to the container or the air, and heat capacities constant over the interval. The mixture mode assumes no change of state occurs; for ice in hot water, the m·L term is computed separately (change-of-state mode). The values of c and L are entered.

Equilibrium temperatureMixed, 1 kg of water at 80 °C and 1 kg of copper at 20 °C settle near 75 °C, not 50 °C.

Mixed, 1 kg of water at 80 °C and 1 kg of copper at 20 °C settle near 75 °C, not 50 °C. The average is weighted by the heat capacities m·c, not by the masses; water (c ≈ 4184) weighs eleven times more than copper (c ≈ 385).