Explanation

(a) 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,
$\Rightarrow$ $\frac{60 - 50}{10} = K\left\lbrack \frac{60 + 50}{2} - \theta_{0} \right\rbrack$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ 1 = K(55 - \theta)$ …(i)
In the second case,
$\Rightarrow$ $\frac{60 - 50}{10} = K\left\lbrack \frac{50 + 42}{2} - \theta_{0} \right\rbrack$
$\Rightarrow$ $0.8 = K\lbrack 46 - \theta\rbrack$ …(ii)
Dividing Eq. (i) by Eq. (ii), we get
$\frac{1}{0.8} = \frac{55 - \theta}{46 - \theta}$
or $40 - \theta = 44 - 0.8\theta$
$\Rightarrow$ $\theta = 10$