b
(b) For \(\theta-t\) plot, rate of cooling \( = \frac{{d\theta }}{{dt}} = \) slope of the curve.

At \(P,\frac{{d\theta }}{{dt}} = \tan {\varphi _2} = k({\theta _2} - {\theta _0})\), where k = constant.

At \(Q\frac{{d\theta }}{{dt}} = \tan {\varphi _1} = k({\theta _1} - {\theta _0})\) 

\(\Rightarrow \,\,\,\frac{{\tan {\varphi _2}}}{{\tan {\varphi _1}}} = \frac{{{\theta _2} - {\theta _0}}}{{{\theta _1} - {\theta _0}}}\)