Question

Determine the law that is defined by the statement, “The rate of loss of heat $-\dfrac{dQ}{dt}$ of the body is directly proportional to the temperature difference $∆T=T_2-T_1$ of the body and surrounding”.
(A) Law of thermometry
(B) Newton’s law of cooling
(C) Law of calorimetry
(D) Zeroth law

Answer 1

Hint
According to the given statement, the rate of loss of heat of the body is directly proportional to the temperature difference of the body and surrounding which suggests that during the rate of loss of heat, the body will be cooling down. The cooling of the body will occur when there is a temperature difference between the body and the surrounding.

Complete step by step answer
Let us consider a body of mass $m$ at temperature $T$ whose specific heat is $s$. Also, the temperature of the surrounding is ${{\rm{T}}_0}$ such that ${\rm{T}} > {{\rm{T}}_0}$.
Since there will be loss of heat by the body, let the amount of heat lost by the body in time $dt$ be $dQ$.
Now, Newton’s law of cooling will be represented as,
 $ - \dfrac{{{\rm{dQ}}}}{{{\rm{dt}}}} \propto \left( {{\rm{T}} - {{\rm{T}}_0}} \right)$
$ - \dfrac{{{\rm{dQ}}}}{{{\rm{dt}}}} = {\rm{k}}\left( {{\rm{T}} - {{\rm{T}}_0}} \right)$
Where $k$ is the proportionality constant. Also, the negative sign denotes the loss of heat during the transmission of heat.
Therefore, (B) Newton’s law of cooling is the required solution.

Note
The temperature always transfers from the body at a higher temperature to the body at a lower temperature. Newton’s law of cooling is applicable for a certain range of temperature differences. For Newton’s law of cooling, the temperature difference between the body and the surrounding should be small; not more than .