Explanation

(b) According to Newton’s law of cooling
$\frac{\theta_{1} - \theta_{2}}{t} = K\left\lbrack \frac{\theta_{1} + \theta_{2}}{2} - \theta_{0} \right\rbrack$
In the first case,
$\Rightarrow$ $\frac{80 - 64}{5} = K\left\lbrack \frac{80 + 64}{2} - \theta_{0} \right\rbrack$
$\Rightarrow$ $3.2 = K\left\lbrack 72 - \theta_{0} \right\rbrack$ …(i)
In the second case,
$\Rightarrow$ $\frac{64 - 52}{5} = K\left\lbrack \frac{64 + 52}{2} - \theta_{0} \right\rbrack$
$\Rightarrow$ $2.4 = K\lbrack 58 - \theta_{0}\rbrack$ …(ii)
Dividing Eq. (i) by Eq. (ii), we get
$\frac{3.2}{2.4} = \frac{72 - \theta_{0}}{58 - \theta_{0}}$
$185.6 - 3.2\theta_{0} = 172.8 - 2.4\theta_{0}$
$\Rightarrow$ $\theta_{0} = 16℃$