Question

how to apply newtons law of cooling to problems ?

Answer 1

Dear student,
Find the answer to your query as under:


It is advisable that the student use newton's law of cooling in its differential form which is as under:

$$\begin{gathered} \frac{dT}{dt}=-k(T-T_0) \\ where,k=positivecons\tan t \end{gathered}$$

Now,

if (T-T ₀ ) is large the dT/dt is also large and negative and hence the rate of cooling is also high, this means that the body is kept in an environment where the temperature gradient is high and thus the rate of transfer of heat energy from a body of higher temperature to a body of lower temperature is high and the body is cooling very fast.

When you now integrate the above equation within the given limits then you get the answer that you are looking for.



Regards
Satyendra Singh