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Thermodynamics
Thermodynamics

Newton's Law of Cooling

dTdt=−h(T−Tenv)\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
h
Cooling constant
Depends on surface and medium
1/s
T
Object temperature
Current temperature
K
T_env
Environment temperature
Ambient temperature
K

Derivation

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

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Common questions

What is the Newton's Law of Cooling formula?

Newton's Law of Cooling is written dT/dt = -h(T - Tₑₙᵥ). 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 - Tₑₙᵥ)?

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_env 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 - Tₑₙᵥ).