Question

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

• A. $45°\text{C}$
• B. $20°\text{C}$
• C. $42°\text{C}$
• D. $10°\text{C}$

Answer 1

The correct option is A $45°\text{C}$

According to newtons law of cooling
$\frac{T_1-T_2}{\Delta t}=k[\frac{T_1+T_2}{2}-T_0]$
$\frac{70-60}{5}=k[\frac{70+60}{2}-T_0]$
$\frac{10}{5}=k[65-T_0]...\left(i\right)$
and $\frac{60-54}{5}=k[\frac{60+54}{2}-T_0]$
$\Rightarrow \frac{6}{5}=k[57-T_0]...\left(ii\right)$
By dividing $\left(i\right)$ by $\left(ii\right)$ we have
$\frac{10}{6}=\frac{65-T_0}{37-T_0}$
$\Rightarrow T_0={45}^{\circ }\text{C}$