Lilongwe University Of Agriculture And

Natural Resources
Bunda \ City Campus
The Department Of Basic Sciences
DATE: (24 /03/2024 to 29/03/24) and (31/04/2024 to 5/04/2024)

Newton's Law of Cooling(Thermal

Radiation)
INTRODUCTION
Newton’s law of cooling describes the rate at which an exposed body changes temperature through
radiation, which is approximately proportional to the difference between the object’s temperature
and its surroundings, provided the difference is small. Simply put, a glass of hot water will cool
down faster in a cold room than in a hot room. For the best results, the temperature change must
be small, and the nature of the heat transfer mechanism must not vary. It was published by Sir
Issac Newton during the early 17th century. There are certain limitations to Newton’s law of
cooling such as the temperature of the surroundings is required to be constant throughout the
observation time, and the mode of heat loss from the body must be only in the form of radiations.
It has a wide range of applications ranging from forensic science, Measuring Temperature of a
Heated Metal, Melting Ice-Cream, Cooling Down of Hot beverages and many more.

Learning Outcomes
• To describe the different modes of transfer of heat.
• To identify the variables which affect the cooling rate of a substance.
• To verify Newton’s Law of Cooling.
• To describe the relationship between temperature and time of cooling of objects.
• To study the relationship between the temperature of a hot body and its time of cooling by
plotting a cooling curve.

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 Theory
This Law of Cooling is named after the famous English Physicist Sir Isaac Newton, who
conducted the first experiments on the nature of cooling.

Statement of the Law :

According to Newton’s Law of Cooling, the rate of cooling of a body is directly proportional to
the difference in temperatures of the body (T) and the surrounding (T0), provided the difference in
temperature should not exceed by 300C.
From the above statement,

…………………………………………..….1
For a body of mass m, specific heat s, and temperature T kept in surrounding of temperature T0;

Now, the rate of cooling,

……………………………………...2
Hence,
……………………………………….3
Since the mass and the specific heat of the body are taken as constants,
the rate of change of temperature with time can be written as,

……………………………………….4

The above equation explains that, as the time increases, the difference in temperatures of the body
and surroundings decreases and hence, the rate of fall of temperature also decreases. It can be
graphically represented as,

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 APPARATUS

These are the apparatus for the experiments.

• Computer with internet

• Copper calorimeter
• Stirrer
• Wooden box with a clamp and stand.
• A wooden lid having a hole in the middle.
• Thermometer
• Stopwatch
• Hot water of about 80 °C.

PROCEDURE
NBThis lab session is divided into two parts. The first part will be done this week (24/03/2024 to
29/03/2024) and the other part will be done the following week of (31/04/2024 to 5/04/2024). The
first part of this lab session involves the pre-lab short answer questons and the computer
simulation part. The second part will involve a physical lab session and a prelab structured long
questions done in groups of ten people per programme.

PART 1

Computer Simulation
1. Follow this link to the site where the experiment will be do.
https://amrita.olabs.edu.in/?sub=1&brch=5&sim=21&cnt=4

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 2. You should have a screen like the one below.

3. Select the material of the calorimeter from the drop down list. (aluminum)
4. Select the radius of the calorimeter using the slider. (4 cm)
5. Select the mass of the calorimeter using the slider. (60g)
6. Select the liquid sample from the drop down list. (water)
7. Select the temperature of the preheated liquid using the slider. (100℃)
8. Select the room temperature using the slider. (27℃)
9. Mass of the liquid is fixed as 250 g.
10. Click on the ‘START’ button on the timer to start/stop the experiment.
11. Click on the ‘Show cross section’ button to view the cross section area.
12. Click on the ‘Show graph’ button to view the graph.
13. To redo the experiment, click on the ‘Reset’ button.

RESULTS FOR SIMULATION EXPERIMENT

Fill in the following table of results. For you to fill in the table do as follow. Click (bring the cursor
on the line of the graph which has been produced by the simulator. Get the time coordinate and
the temperature of water in calorimeter, T (℃). Record in the table 1.1.

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Table 1.1: A table of results for Newtons Cooling
SNo Time for Temperature of water Temperature of water Difference of
cooling in calorimeter, T (℃)
in enclosure,𝑇0 Temperature,(T-𝑇0)
t(min.)
((℃) (℃)
1 0 100 30 70.00

2 6
3 9
4 15
5 19
6 24
7 29
8 34
9 38

10 49
11 52

12 58
13 60
14 69
15 76
16 82
17 94
18 100
Using the results from table 1.1. Plot a graph of Temperature of water in calorimeter, T ((℃)
against time for cooling t (min) in excel.

PART 2

Physical Lab procedure/ Real Lab Procedure:

1. Fill about 2/3rd of the copper calorimeter containing stirrer with hot water of about 80 °C

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 2. Place the calorimeter inside the wooden box. The space between the wooden box and
calorimeter is filled with cotton to avoid heat loss.
3. Close the wooden box with its lid.
4. Suspend the thermometer inside the hot water in the calorimeter from the clamp and stand.
5. Stir water continuously to make it cool uniformly.
6. When the temperature of hot water falls to 70°C, start the stopwatch.
7. Note the temperature reading every five minutes.
8. Continue the time temperature observation till the temperature becomes constant.
9. Plot a graph between time along X-axis and temperature along Y-axis. This graph is called
the cooling curve.
10. The graph is an exponential curve, and it shows that the temperature falls quickly at the
beginning and then slowly as the difference in temperature goes on decreasing. This verifies
the Newton’s Law of cooling.

RESULTS FOR PHYSICAL LAB XPERIMENT

Create a table of results as given in table 1.1 and record your results in there.
Consider the following:

1. Temperature of water in the enclosure is found to be a constant. If not, then take its mean
as T0.
2. From the observations, we can calculate the temperature difference (T-T0).
3. Now, plot a graph between time (t) and temperature (T), taking time along X axis and
temperature along Y axis.

DISCUSSION
Discuss your results of the plotted graph in terms of how they support or falls in line with the
Newtons’ cooling law. Also discuss the significance of the three peaks of your graph and how they
help you explain the Newton’s Law of Cooling.

PRELAB QUESTIONS INDIVIDUAL WORK

1. Define the temperature of a body?

2. Which is the law that explains the relation of the cooling of a body with its surrounding
temperature?
3. Name the process which cannot be retraced in the reverse direction?

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 4. What is meant by the rate of cooling ?
5. What is the shape of the Time Vs Temperature graph of a hot body cooling under normal
temperature?
6. What is the significance of Newton’s cooling curve?
7. Two identical bodies of temperature 800C are kept in two containers of temperatures 100C
and 600C respectively. Which among them cools first?
8. Express Newton’s Law of Cooling in mathematical form?

PRELAB QUESTIONS GROUP WORK FOR TEN PEOPLE PER GROUP PER
PROGRAMME

1. A thermometer is taken from a room that is 20OC to the outdoors where the temperature is 5OC.
After one minute, the thermometer reads 12OC. Use Newton s Law of Cooling to answer the
following questions.
(a) What will the reading on the thermometer be after two more minute?

(b) When will the thermometer read 7OC ?

2. At Midnight with the temperature inside your house at 70F and the temperature outside at 20 F,
your furnace breaks down. Two hours later, the temperature in your house has fallen to 50 F.
Assume that the outside temperature remains constant at 20 F. At what time will the inside
temperature of your house reach 40 F ?
3. You can find the temperature inside your refrigerator without putting a thermometer inside.
Take a can of soda from the refrigerator, let it warm for half an hour, then record its temperature.
Let it warm for another half an hour and record its temperature again. Suppose that the readings
are T (1=2) = 45F and T (1) = 55 F. Assuming that the room temperature is 70 F, what is the
temperature inside the refrigerator?
4. In a murder investigation, a corpse was found by a detective at exactly 7 P.M. Being alert, the
detective also measured the body temperature and found it to be 70 F. Three hours later, the
detective measured the body temperature again and found it to be 60 F. If the room temperature is
50 F, and assuming that the body temperature of the person before death was 98:6 F, at what time
did the murder occur?

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5. John and Maria are having dinner and each orders a cup of coffee. John cools his coffee with
three tablespoons of cream. They wait ten minutes and then Maria cools her coffee with three
tablespoons of cream. The two then begin to drink. Who drinks the hotter coffee?(Assume that
adding three tablespoons of cream to coffee immediately cools the coffee by 10 F.)

Further reading
1. Laboratory Manual Physics for class XI - Published by NCERT
2. http://epathshala.nic.in/wpcontent/doc/book/flipbook/Class%20XI/11087Physics%20Par
t%20II/ch%2011/index.ht ml

NB : ALL REPORTS BE TYPED STRICTLY AND

PRINT TOGETHER WITH ITS SOURCE CODE
IN LATEX FILE.

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