Physics - Heat & Thermo Question with Solution | TestHub

Newton's law of cooling states that 

$\frac{\left(T_1-T_2\right)}{t}=K\left(\left(\frac{T_1+T_2}{2}\right)-T_0\right) ...\left(i\right)$

where $T_0$ is the temperature of the surrounding. From equation (i),

$\frac{60-40}{7\times 60}=K\left(\frac{60+40}{2}-10\right)$

$$\begin{gathered} \Rightarrow \frac{20}{7\times 60}=40K \\ \Rightarrow K=\frac{20}{7\times 60\times 40} \end{gathered}$$

Let the temperature of the body after the given time be $x °\mathrm{C}$. By Newton's law of cooling,

$$\begin{gathered} \frac{40-x}{7\times 60}=K\left(\frac{40+x}{2}-10\right) \\ \Rightarrow \frac{40-x}{7\times 60}=\frac{1}{14\times 60}\left(\frac{20+x}{2}\right) \\ \Rightarrow 160-4x=20+x \\ \Rightarrow x=28 °\mathrm{C} \end{gathered}$$