AP/IB Physics Lab Newton's Law of Cooling

Introduction

Cooling of a heated body takes place by conduction, convection, and radiation of heat to the air and surrounding objects. The rate of heat loss, Q/ t, is proportional to the temperature difference, T. Q is the heat lost in a time interval, t. We will assume that the substance has a constant heat capacity and that the rate of cooling will be proportional to the temperature difference between the object and the surroundings. This is Newton's Law of Cooling.

We can express this law as                

Eq. 1      D/ t = -KD        

where D is the temperature difference between an object and its surroundings. K depends on several factors, but is constant for any one situation. Another way to express this "decay" of temperature is with the equation          

 Eq. 2     D = Doe-Kt         

where Do is the initial temperature difference at t = 0. Equation 2 can also be expressed as

Eq. 3     ln D = -Kt + ln Do  

Thus, a plot of ln D versus time t should be a straight line with a slope equal to -K.

Materials: beaker, hot plate, thermometer, timer, string, clamp and ring stand

Procedures

1. Record room temperature.

2. Obtain a beaker of warm water approximately 500 C. Place the beaker on thetable with the thermometer in it, using a piece of string to suspend the thermometer from the clamp. Be sure the bulb of the thermometer is "centered" in the water.

3. Allow a minute for the thermometer and water to reach equilibrium.

4. Record the temperature and the precise time.

5. After this first reading, record the temperature every two minutes for 60 minutes.

6. At the end, take another reading of room temperature. Be sure to allow time for the zeroth law to take effect.

Analysis

1. Make a graph of temperature difference versus time on regular graph paper. At each of two points about 30 minutes apart, determine the slope of the graph by drawing a line tangent to the curved line and determining the slope of the tangent.

2. For each point substitute values into equation 1 and solve for K. Compare the two values.

3. Plot the temperature difference D versus time t on two cycle semilog graph paper. Find K by determining the slope of the line where the coordinates of the points used for the slope calculation are (t1, D1) and (t2, D2).  Compare this K value with that found using equation 2.

4. How is the rate of cooling similar to and different from radioactive decay?