Question

A body takes $10$ minutes to cool down from $62^{\circ }C$ to $50^{\circ }C$. If the temperature of surrounding is $26^{\circ }C$ then in the next 10 minutes temperature of the body will be:

• A. $38^{\circ }C$
• B. $40^{\circ }C$
• C. $42^{\circ }C$
• D. $44^{\circ }C$

Answer 1

Answer: (C)

From Newton's cooling law
$\frac{{\theta }_1-{\theta }_2}{t}=K\left(\frac{{\theta }_1+{\theta }_2}{2}-26\right)$
Case I : $\frac{12}{10}=K\times 30$
$K=\frac{12}{10\times 30}$
$=\frac{1}{25}$
Case II : $\frac{50-{\theta }_2}{10}=K\left(\frac{50+{\theta }_2}{2}-26\right)$
$\frac{\left(50-{\theta }_2\right)}{10}=\frac{1}{25}\left(\frac{{\theta }_2-2}{2}\right)$
$250-5{\theta }_2={\theta }_2-2$
$6{\theta }_2=252$
${\theta }_2=\frac{252}{6}$
$=42^{\circ }C$