Newton's Law of Cooling

\frac{dT}{dt} = -h(T - T_{env})

Rate of cooling proportional to temperature difference. Solution: T(t) = T_env + (T₀ - T_env)e^(-ht).

Variables

dT/dt

Rate of temperature change

Cooling rate

K/s

Cooling constant

Depends on surface and medium

1/s

Object temperature

Current temperature

T_env

Environment temperature

Ambient temperature

Derivation

Empirical law for convective cooling. Valid when temperature difference is small.

Your notes

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Where this formula is listed

Thermodynamics formulas, under Heat & Temperature, alongside Heat Capacity, Latent Heat, Linear Thermal Expansion, Volume Thermal Expansion and Thermal Resistance.
In the thermodynamics list it comes after Thermal Resistance and before First Law of Thermodynamics.
Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Newton's Law of Cooling formula?

Newton's Law of Cooling is written dT/dt = −h(T − T_env). Rate of cooling proportional to temperature difference. Solution: T(t) = T_env + (T₀ - T_env)e^(-ht). It belongs to Thermodynamics, under Heat & Temperature.

What are the units in dT/dt = −h(T − T_env)?

In SI units, dT/dt is rate of temperature change, measured in K/s; h is cooling constant, measured in 1/s; T is object temperature, measured in K; T_e nv is environment temperature, measured in K.

How is the Newton's Law of Cooling formula derived?

Empirical law for convective cooling. Valid when temperature difference is small. The result is dT/dt = −h(T − T_env).