# Newton's Law of Cooling

- Author:
- Tim Brzezinski

- Topic:
- Differential Equation

Suppose a very hot object is placed in a cooler room.
Or suppose a very cool object is placed inside a much hotter room.
, where

**Newton's Law of Cooling**states that the**rate of change of temperature of an object**is**directly proportional****to the DIFFERENCE BETWEEN the****current temperature of the object****& the****initial temperature of the object.**In differential equations, this is written as*T*= the current temperature of the object,**&***R*= the temperature of the surrounding medium (room),*k*= some constant of proportionality (a value for which you'll often have to solve).**Calculus Students:**You can use this applet as a reference in checking your solution to any differential equation you solve that relates to Newton's Law of Cooling. (The function appears in the upper left-hand corner.)**PreCalculus & Calculus Students:**You can use this applet as a reference to check your work in solving application problems that relate to evaluating exponential functions and/or solving exponential equations within this context. You can enter the following information on the right side:**Initial Temperature of the Object****One Data Point: (n, temperature after n minutes)**After doing so, you can enter in any**time value**or**temperature value**and interpret the meaning of the other coordinate in the corresponding point that appears in the graph on the left.