Heat formulas
Heat Q is the energy a body gains or loses by heat transfer, measured in joules (1 kJ = 1000 J, 1 cal ≈ 4.19 J).
- Heating and cooling: Q = c·m·(t₂ − t₁), c is the specific heat in J/(kg·°C): water 4200, ice 2100, steam about 2000.
- Melting and freezing: Q = λ·m at the melting point; λ is the latent heat of fusion (ice: 3.4·10⁵ J/kg).
- Boiling and condensation: Q = L·m at the boiling point; L is the latent heat of vaporization (water: 2.3·10⁶ J/kg).
- Fuel combustion: Q = q·m; with heater efficiency η the useful heat is η·q·m.
Stages: ice → water → steam
When the phase changes, split the process into stages. Turning 2 kg of ice at −10 °C into steam at 100 °C: Q₁ = 2100·2·10 = 42 kJ, Q₂ = 3.4·10⁵·2 = 680 kJ, Q₃ = 4200·2·100 = 840 kJ, Q₄ = 2.3·10⁶·2 = 4600 kJ; total 6162 kJ. On the t(Q) graph phase changes are flat plateaus.
Heat balance equation
In an insulated system Q₁ + Q₂ + … + Qₙ = 0 (cooling bodies have Q < 0). 2 kg of water at 20 °C plus 3 kg at 70 °C: 4200·2·(θ − 20) + 4200·3·(θ − 70) = 0 → θ = 50 °C. With ice, check first whether there is enough heat to melt it; if not, the mixture stays at 0 °C and the calculator shows how much ice melted.
Reference data
c, λ, L and q come from school tables; university handbooks differ slightly (e.g. water L = 2.26·10⁶ J/kg). If your problem gives its own values, use the “Formula” tab.