# physics-lab-6-newtons-law-of-cooling

Lab 6

Newton’s law of
Cooling

1. Objective:

The purpose of this experiment is to use
Newton’s law of cooling to obtain a value for the time constant of a metal
thermometer and a glass thermometer.

2. Equipment:

Metal stem dial thermometer, mercury-in-glass
thermometer, a candle, a lighter, a stop watch.

3. Theory:

Newton’s law of cooling states that the
rate at which an object loses heat is directly proportional to the excess
temperature between the object and the surrounding. If a thermometer is heated
to a temperature To and allowed to cool, its temperature T at any
time t can be expressed using Newton’s law as:

T – Tr = (To – Tr)e–t/t (i)

Here Tr is the room temperature and
t is called the time constant of the thermometer. In the above
equation, when t =t, it can
be shown that

T – Tr = 0.37(To – Tr)

This means thatt is the time taken for the temperature of the thermometer to fall
from To to 0.37To. Using this,t can be obtained from a graph of temperature of the thermometer
against time.

Equation (i) can also be written as

.0/msohtmlclip1/01/clip_image002.gif”> (ii)

4. Procedure:

Heat the metal thermometer to its maximum
range by using a lighted candle. Move the candle flame around so that the stem
of the thermometer gets uniformly heated. Remove the candle and start the stop
watch. Measure the temperature shown by the thermometer dial every 5 seconds
for the first 30 seconds and then every 10 seconds until the temperature falls
thermometer given to you is marked in oF and you should convert the
temperature to oC using the relation:

.0/msohtmlclip1/01/clip_image004.gif”>

Tabulate your data a s follows:

To = …….oC Tr
= ……..oC

 Time (s) Temp (oF) Temp T(oC) T – Tr Ln(T – Tr)

5. Interpretation
of data:

1. Draw a graph of T against
t and obtain the time t corresponding to 0.37To. This is the value oft.

2. Write equation (ii)
in the y = mx + b form and identify the variable x and y. Use this equation to
draw a suitable graph of the data. Measure the slope and the y-intercept of
your graph. Obtain a value oft from the

3. Obtain the percent
difference between the values in 1 and 2.

5. Questions:

1. Two objects are
heated 120oC and 300oC respectively. According to
Newton’s law of cooling, which of these two objects will cool faster? Why?

2. At 7:00 pm the
police discovered a body in a hotel room which maintained a constant
temperature of 24oC. At the time of discovery, the temperature of
the dead body was 36oC. After 4 hours the temperature of the body
fell to 30oC. Use Newton’s law of cooling to approximate the time of
death.

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