Experimental Verification of Newton's Law of Cooling - QS Study
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Let consider a spherical calorimeter of mass m whose outer surface is blackened. It is filled with hot water of mass m1. The calorimeter with a thermometer is suspended from a stand (Fig).


The calorimeter and the hot water radiate heat energy to the surroundings. Using a stop clock, the temperature is noted for every 30 seconds interval of time till the temperature falls by about 20° C. The readings are entered in a tabular column.

If the temperature of the calorimeter and the water falls from T1 to T2 in t seconds, the quantity of heat energy lost by radiation Q = (ms + m1s1) (T1 – T2), where s is the specific heat capacity of the material of the calorimeter s1 is the specific heat capacity of water.

Rate of cooling = Heat energy lost / time taken

so, Q/t = (ms + m1s1)(T1 – T2) / t

If the room temperature is T0, the average excess temperature of the calorimeter over that of the surroundings is [{(T1 + T2)/2) – T0]

According to Newton’s Law of cooling, Q/t α [{(T1 + T2)/2) – T0]

[Q/t = (ms + m1s1)(T1 – T2) / t] α [{(T1 + T2)/2) – T0]

so, [(ms + m1s1)(T1 – T2)] / [t.{(T1 + T2)/2 – T0}] = Constant

The time for every 4° fall in temperature is noted. The last column in the tabular column is found to be the same. This proves Newton’s Law of cooling.