Calculators/Physics/Heat and heat balance

Heat and heat balance

Q = mcΔT · phase changes · mixture temperature

Heat and heat balance — illustration
Heat Q
210,000 J

Q = m·c·ΔT. The specific heat c tells you how much energy is needed to warm 1 kg of a substance by 1 K. Water has a high c (4200) — it stores a lot of heat.

Three thermodynamics calculations. The heat of warming depends on mass, specific heat and the temperature change:

Q=m c ΔTQ=m\,c\,\Delta T

The heat of a phase change (melting, vaporisation) occurs at constant temperature: Q=m LQ=m\,L. The final temperature of a mixture of two bodies follows from the heat balance (heat released = heat absorbed):

Tk=m1c1T1+m2c2T2m1c1+m2c2T_k=\frac{m_1 c_1 T_1+m_2 c_2 T_2}{m_1 c_1+m_2 c_2}

The calculator has specific-heat presets (water 4200, aluminium 900, iron 450 J/kg·K).

Examples

Warming 1 kg of water by 50 K
→ Q = 1·4200·50 = 210,000 J
Melting 1 kg of ice (L = 334,000)
→ Q = 334,000 J (the temperature does not change)
Mixing 1 kg of water at 80°C + 0.5 kg at 20°C
→ T_k = 60°C

Frequently asked questions

Why does water warm up so slowly?+

It has a high specific heat (4200 J/kg·K) — a lot of energy is needed to warm it. That is why it moderates climate: seas warm up slowly and cool down slowly.

Why doesn't the temperature rise during melting?+

Because the supplied heat breaks the bonds between molecules (changes the state of matter) instead of increasing their kinetic energy. Hence Q = mL at constant temperature.

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