Explanation

(b) According to Newton’s law $\frac{\theta_{1} - \theta_{2}}{t} = k\left\lbrack \frac{\theta_{1} + \theta_{2}}{2} - \theta_{0} \right\rbrack$
Initially,
$\frac{(80 - 64)}{5} = K\left( \frac{80 + 64}{2} - \theta_{0} \right) \Rightarrow 3.2 = K(72 - \theta_{0})\ \ ...(i)$
Finally
$\frac{(64 - 52)}{10} = K\left\lbrack \frac{64 + 52}{2} - \theta_{0} \right\rbrack \Rightarrow 1.2 = K\lbrack 58 - \theta_{0}\rbrack\ \ \ ...(ii)$
On solving equation (i) and (ii), $\theta_{0} = 49℃$