Q. 75.0( 1 Vote )

Newton’s law of cooling is a special case of
A. Wien’s displacement law

B. Kirchhoff’s law

C. Stefan’s law

D. Planck’s law

Answer :

Newton’s law of cooling is a special case of Stefan’s law.
Stefan’s Law states that:
The energy of thermal radiation emitted per unit time by a body having surface area A is given as:

Now, the energy absorbed by a body due to radiations emitted by the walls per unit time is given as:

Here T0 is the temperature of the surrounding.
Now the net rate of loss of energy of the body due to thermal radiation is:

If the temperature difference is small, we can write

Using Binomial Expansion for the forth power we get and using equation relating heat and specific heat we get,

For a small difference in temperature of the body and the surroundings, the rate of cooling is directly proportional to the Area exposed of the body and the temperature difference.
It can also be written as,

This is Newton’s Law of Cooling. b is a constant and depends on the nature of the surface and surrounding conditions.
Negative sign shows that the temperature decrease with time.
Hence. We started off with Stefan’s Law and Ended with Newton’s Law of cooling.
Thus, option (c) is the correct option.

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