Newtons Law of Cooling Calculator

Newton's Law of Cooling

Newton's law of cooling models how an object's temperature approaches the surrounding environment. The rate of change is proportional to the temperature difference, producing exponential decay toward ambient temperature.

Formula

$$T(t) = T_a + (T_0 - T_a)\,e^{-kt}$$

$T_0$ is the initial temperature, $T_a$ is ambient temperature, $k$ is the positive cooling constant, and $t$ is elapsed time. Larger $k$ means faster cooling.

Practical Notes

This model works well for small temperature differences and forced convection. It assumes a constant ambient temperature and linear heat transfer coefficient. For large swings or phase changes, more detailed thermal models are needed.

Related tools: Enthalpy Calculator and Bulk Modulus Calculator.

Frequently Asked Questions

What does the cooling constant k represent?

k combines heat transfer effects such as surface area, convection, and thermal properties. Higher k means the object cools faster.

What are the units of k?

k has units of inverse time (for example, 1/s) when time is in seconds. Match time units consistently in your calculation.

Can temperature rise instead of fall?

Yes. If the object starts colder than ambient, it warms toward $T_a$ using the same exponential form.

What is the half-life of cooling?

Half-life is $t_{1/2} = \ln(2)/k$, the time for the temperature difference from ambient to halve.

When does Newton's law break down?

Large temperature gradients, radiation dominance, or changing ambient conditions can make the simple exponential model inaccurate.

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Newtons Law of Cooling Calculator