Question

According to Newton's law of cooling, the rate of cooling of a body is proportional to $(\Delta \theta {)}^n$, where $\Delta \theta$ is the difference of the temperature of the body and the surroundings, and $n$ is equal to

• A. two
• B. three
• C. four
• D. one

Answer 1

The correct option is D one

Newton's law of cooling states that the rate of cooling of a body is directly proportional to the temperature difference between the body and the surroundings. It can be derived from the conservation of energy principle.

The energy lost by the body in unit time must be transferred to the surroundings. Therefore,

$\rho c\frac{dT}{dt}=k(T-T_{ambient})=k\Delta \theta \Rightarrow \frac{d\theta }{dt}=\frac{dT}{dt}\propto K\Delta \theta$.

Since ambient temperature remains constant.

$\rho$ is density and $c$ is specific heat capacity of the body.