Question

A black body calorimeter filled with hot water cools from ${60}^{\circ }C$ to ${50}^{\circ }C$ in $4min$ and ${40}^{\circ }C$ to ${30}^{\circ }C$ in $8min$. The approximate temperature of surrounding is :

• A. ${10}^{o}C$
• B. ${15}^{o}C$
• C. ${20}^{o}C$
• D. ${25}^{o}C$

Answer 1

The correct option is A ${10}^{o}C$

Assuming the temperature of surrounding be $t^{o}C$

CASE-1

$\frac{(60-50)}{4min}=k(55-t)\left(1\right)$

Again, CASE-2

$\frac{(40-30)}{8min}=k(35-t)\left(2\right)\frac{\left(1\right)}{\left(2\right)}=\frac{\frac{10}{4}}{\frac{10}{8}}=\frac{(55-t)}{(35-t)}\Rightarrow 2(35-t)=55-t\Rightarrow 70-2t=55-t\Rightarrow t=15℃$