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 from $46{}^{\circ }C$ 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

Answer: (B)

According to Newton's law of cooling
$\frac{{\theta }_1-{\theta }_2}{t}\propto \left[\frac{{\theta }_1+{\theta }_2}{2}-\theta \right]$
For the first condition
$\frac{62-61}{T}\propto \left[\frac{62+61}{2}-30\right]$ (i)
And for the second condition
$\frac{46-45.5}{t}\propto \left[\frac{46+45.5}{2}-30\right]$ (ii)
By solving equation (i) and (ii), we get t = T minutes.