Question

A body cools from $70$${}^o$C to $50$${}^o$C in $5$ minutes. Temperature of surroundings is $20$${}^o$C. Its temperature after next $10$ minutes is

• A. ${26}^{o}C$
• B. ${30}^{o}C$
• C. ${35}^{o}C$
• D. ${45}^{o}C$

Answer 1

The correct option is A ${26}^{o}C$

Newton's cooling law $\frac{d\theta }{dt}=-k(\theta -{\theta }_0)$

putting the given values of the situation in the formula we get:-

$\frac{(70-50)}{5}=-k(70-20)$

$=>\frac{20}{5}=-k\left(50\right)$

$=>-k=\frac{2}{25}$

now, cooling body at $50{}^{0}C$ for 10 min

let temperature after 10 min be T

$\frac{(50-T)}{10}=\frac{2}{25}(50-20)$

$\frac{(50-T)}{10}=\frac{12}{5}$

$50-T=24$

$T=50-24$

$T={26}^{0}C$