Question

A body takes $T$ minutes to cool from ${62}^{\circ }C$ to ${61}^{\circ }C$ when the surrounding temperature is ${30}^{\circ }C$. The time taken by the body to cool form ${46}^{\circ }C$ to ${45.5}^{\circ }C$ is

• A. Greater than T minutes
• B. Equal to T minutes
• C. Less than T minutes
• D. None of these

Answer 1

The correct option is B

Equal to T minutes

According to Newton's law of cooling

$\frac{{\theta }_1-{\theta }_2}{t}$ $⋉$ $[\frac{{\theta }_1+{\theta }_2}{2}-\theta ]$

For the first condition

$\frac{62-61}{T}$ $⋉$ $[\frac{62+61}{2}-30]$ .............(i)

and for the second condition

$\frac{46-45.5}{t}$ $⋉$ $[\frac{46+45.5}{2}-30]$ .............(ii)

By solving Eqs.(i) and (ii), we get $t$ = $T$ minutes.