HOTTER OBJECT entering a COOLER ROOM

COOLER OBJECT entering a HOTTER ROOM

Home Newton’s Law of Cooling

HOTTER OBJECT entering a COOLER ROOM

COOLER OBJECT entering a HOTTER ROOM

Suppose a very hot object is placed in a cooler room.

Or suppose a very cool object is placed inside a much hotter room.

**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 * dT/dt=k(T-R) *, where

*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.