c
(c) \(\frac{{{\theta _1} - {\theta _2}}}{t} = K\left[ {\frac{{{\theta _1} + {\theta _2}}}{2} - {\theta _0}} \right]\)

In the first 10 minute

\(\frac{{62 - 50}}{{10}} = K\,\left[ {\frac{{62 + 50}}{2} - {\theta _0}} \right]\)

==> \(1.2 = \,K\,[56 - {\theta _0}]\) .... \((i)\)

\(\frac{{50 - 42}}{{10}} = K\,\left[ {\frac{{50 + 42}}{2} - {\theta _0}} \right]\)

==> \(0.8 = \,K\,[46 - {\theta _0}]\) .... \((ii)\)

from equations \((i)\) and \((ii)\)

\(\frac{{1.2}}{{0.8}} = \frac{{(56 - {\theta _0})}}{{(46 - {\theta _0})}}\)

==> \({\theta _0} = 26^\circ C\)