If a metallic sphere gets cooled from ${62^o}C$ to ${50^o}C$ in ${40^o}C$and in the next $10\;\min utes$gets cooled to ${42^o}C$, then the temperature of the surroundings is ......... $^oC$
Diffcult
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(c) $\frac{{{\theta _1} - {\theta _2}}}{t} = K\left[ {\frac{{{\theta _1} + {\theta _2}}}{2} - {\theta _0}} \right]$
In the first 10 minute
$\frac{{62 - 50}}{{10}} = K\,\left[ {\frac{{62 + 50}}{2} - {\theta _0}} \right]$
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 $(ii)$
$\frac{{1.2}}{{0.8}} = \frac{{(56 - {\theta _0})}}{{(46 - {\theta _0})}}$
==> ${\theta _0} = 26^\circ C$
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