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Newton's Law of Cooling

physics thermodynamics
Table of Contents

Newton’s law of Cooling says that the rate of change of temperature of an object is proportional to the difference between the object’s temperature and the ambient temperature.

It is given by:

$$ \frac{dT}{dt} = -k(T - T_{\text{env}}) $$

Where

  • \( \frac{dT}{dt} \) is the rate of change of temperature with respect to time,
  • \( T \) is the temperature of the object at time \( t \),
  • \( T_{\text{env}} \) is the ambient (surrounding) temperature, and
  • \( k \) is the cooling rate constant.

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