Question

A body takes $4\text{minute}$ to cool from ${61}^{\circ }\text{C}$ to ${59}^{\circ }\text{C}$. If the temperature of the surroundings is ${30}^{\circ }\text{C}$, the time taken by the body to cool from ${51}^{\circ }\text{C}$ to ${49}^{\circ }\text{C}$ is :

• A. $8\text{min.}$
• B. $3\text{min.}$
• C. $4\text{min.}$
• D. $6\text{min.}$

Answer 1

The correct option is D $6\text{min.}$

The change in temperature per unit time is given by Newton's law of cooling which is,

$\frac{\Delta T}{\Delta t}=K(T_t-T_s)$

$T_t=\text{average temp.}$ and $T_S=\text{surrounding temp.}$

$\frac{61-59}{4}=K(\frac{61+59}{2}-30)...\left(1\right)$

$\frac{51-49}{t}=K(\frac{51+49}{2}-30)...\left(2\right)$

Divide equation $\left(1\right)$ to $\left(2\right)$,

$\frac{t}{4}=\frac{60-30}{50-30}=\frac{30}{20}$

So, $t=6\text{minutes}$.

Hence, option $\left(\text{D}\right)$ is correct.