Dear students we are familiar about the principle of exchange of heat. Amount of heat lost by substance 1 is always same as the amount of heat gained by substance 2. Also from the concept of specific heat capacity we can say that the heat needed to raise the temperature of substance is directly proportional to the difference in temperature of substance and surrounding.
In similar way the heat lost by substance also depends upon the difference in temperature of substance and surrounding, which was explained in detail in Newton’s law of cooling.
Let us understand the concept in detail.
Let’s understand concept of Newton’s law of cooling….!
Newton’s law of cooling:-
The rate of loss of heat by a body is directly proportional to the excess of temperature of the body over the surroundings, provided that this excess is small.”
Where ‘k’ is constant of proportionality
OR The rate of fall of temperature of body is directly proportional to the excess of temperature of the body over the surroundings, provided that this excess is very small.
Where K′= K/ms, in which m is mass of the body and ‘s’ is the specific heat of the body.
Suppose the water is heated up to T 0C and filled in calorimeter allowed to cool by its own. The time for cooling and corresponding temperature is recorded and the graphs as plotted.
The following graph 1 the variation of temperature with time is shown and in graph 2 rate of cooling vs difference in temperature of substance and surrounding is shown.
From graph 2, Newton’s law of cooling can be verified
Let’s solve some numerical for more detail….!
Ex: Hot metal sphere of temperature cools from 85 0C to 75 0C in 20 min. Find the temperature of sphere in next 20 min, if the temperature of surrounding is 25 0C.
Solution: T1 =(85 +75)/2=80 0C, t1=20 min, T0=25 0C
Where T= temperature of sphere after next 20 min.
By Newton’s law of cooling,
∴ k = 1/110
For 2nd case,
∴ T = 66.670 C