# Newton's Law of Cooling

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 , 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.