Page 119 - Physics - XI

rate of cooling, dQ ms d ( )
dt dt 0
d d k
or ms k ( ) or ( ) …(1)
dt 0 dt ms 0

where k is the constant of proportionality.
dθ = –K (θ – θ ) …(2)
dt 1 0
k
As m and s are also constants for the given body, hence K = ms is another constant.
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Equation (2) can be written as
d = –K dt …(3)

0 1
Now, on integrating the equation (3) on both sides we have
d

= Kdt
1
0
log (θ – θ ) = – K t + C …(4)
1
0
where C is the constant of integration.

If we plot a graph between log (θ – θ ) and t, it will be a straight line. This is verifi ed from equation (4).
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One should keep in mind that Newton's law of cooling holds good for the temperature diff erence between
the body and its surroundings should not be more than 30°C. Hence, (θ – θ ) should not be more than 30°C.
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Procedure

1. Clean the Newton's law of cooling apparatus and fi ll the space between its two walls with water which
acts as surroundings at constant temperature θ .
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2. Take two thermometers and compare them by measuring the temperature of the same water contained
in a beaker by both thermometers. Consider one of them, say A, to be the standard thermometer. Find
the correction to be applied to the other, say B. Suspend thermometer B in water contained in the
double-walled enclosure as shown in Fig. 6.1.
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3. Heat water in a beaker to a temperature of about 40°C above the room temperature and fi ll th of
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calorimeter C with this hot water. Place the lid and stirrer S in proper position and suspend thermometer
A in hot water in the calorimeter as shown in Fig. 6.1.

4. Note the temperature of water in double walled vessel with the help of thermometer B when the
diff erence of readings on the two thermometers is about 30°C.

5. Note the reading of thermometer A and simultaneously start the stopwatch. Gently stir the hot water
and note the reading of thermometer A after every one minute. After about 5 readings, increase the time
interval between successive readings to two minutes.
6. Keep on taking the readings of thermometer A till the temperature of hot water is about 5°C above the
room temperature.

7. Again note the temperature of water in double-walled vessel with thermometer B and fi nd the mean
temperature θ of this water.
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