Question

Certain quantity of water cools from ${70}^{o}C$ to ${60}^{o}C$ in the first $5$ minutes and to ${54}^{o}C$ in the next $5$ minutes. The temperature of the surroundings is ;

• A. ${45}^{o}C$
• B. ${20}^{o}C$
• C. ${42}^{o}C$
• D. ${10}^{o}C$

Answer 1

The correct option is A ${45}^{o}C$

$\frac{60-70}{5}=-K(65-T)$

$\frac{54-60}{5}-K(57-T)$

$\frac{-10}{-6}=\frac{65-T}{57-T}$

$285-5T=195-3T$
$90=2T$
$T={45}^o$