Calorimetry calculator
Q = m·c·(T₂ − T₁)
Three calorimetry calculations: the heat to warm or cool a mass (Q = m·c·ΔT, with a received/released verdict), the energy of a phase change (Q = m·L), and the equilibrium temperature when two bodies are mixed. Each with its worked calculation, its conversions (kJ, Wh) and its assumptions displayed: isolated system, constant capacities, no phase change during mixing.
334700 J
- Calculation
- Q = m·c·ΔT = 1 × 4184 × 80 = 334700 J
- kJ / Wh
- that is 334.7 kJ, that is 92.98 Wh (1 Wh = 3600 J exactly)
Q > 0: the body receives 334700 J: this energy must be supplied to heat it.
Scientific dossier
What the tool computes, what it assumes, where it stops being valid, and where its data comes from.
Method & formulasQ = m·c·(T₂ − T₁)
Q = m·c·(T₂ − T₁)
Q = m·L
T_eq = (m₁c₁T₁ + m₂c₂T₂) / (m₁c₁ + m₂c₂)
The first formula is the definition of specific heat capacity: c joules to raise 1 kg by 1 K. The equilibrium temperature comes from writing that the heat released by the hot body equals the heat received by the cold one (isolated system): it is an average of the temperatures weighted by the capacities m·c. Since these formulas are linear in temperature, they give the same result in °C and in K, as long as the two units are not mixed within one calculation.
- Sign convention
- · Q > 0: energy received by the body (it warms up, or melts); Q < 0: energy released (it cools down). The sign comes out of the calculation through ΔT, nothing to decide by hand.
- 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, defined as exactly 4.184 J.
- Latent heat (L)
- · the phase-change energy per kilogram, at constant temperature: the melting or boiling plateau, where supplied heat no longer raises the temperature.
Validity domainThe calculation assumes an isolated system (no losses to the container or the air, which is never exactly true in a real calorimeter) and constant capacities over the interval.
The calculation assumes an isolated system (no losses to the container or the air, which is never exactly true in a real calorimeter) and constant capacities over the interval. The mixture mode assumes NO phase change occurs between the two temperatures: mixing ice with hot water requires adding the m·L term yourself (phase-change mode), the tool does not do it on its own. No value of c or L is imposed: you enter the one from your textbook or table.
Common pitfall: equilibrium is not the average of the temperaturesMixing 1 kg of water at 80 °C with 1 kg of copper at 20 °C does not give 50 °C: water (c ≈ 4184) weighs eleven times more than copper (c ≈ 385) in the average, and equilibrium settles near 75 °C.
Mixing 1 kg of water at 80 °C with 1 kg of copper at 20 °C does not give 50 °C: water (c ≈ 4184) weighs eleven times more than copper (c ≈ 385) in the average, and equilibrium settles near 75 °C. The equilibrium temperature is an average weighted by the capacities m·c, not by the masses. It is the simple average only when the two m·c products are equal.