The initial temperature of a body is $80°C$ . If its temperature falls to $64°C$ in $5$ minutes and in $10$ minutes to $52°C$ then the temperature of surrounding will be ...... $^oC$
Diffcult
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(b) According to Newton's law $\frac{{{\theta _1} - {\theta _2}}}{t} = k\left[ {\frac{{{\theta _1} + {\theta _2}}}{2} - {\theta _0}} \right]$
Initially,
$\frac{{(80 - 64)}}{5} = K\,\left( {\frac{{80 + 64}}{2} - {\theta _0}} \right)$ ==> $3.2 = K[72 - {\theta _0}]$ ... $(i)$
Finally
$\frac{{(64 - 52)}}{{10}} = K\,\left[ {\frac{{64 + 52}}{2} - {\theta _0}} \right]$ ==> $1.2 = K[58 - {\theta _0}]$...$(ii)$
On solving equation $(i)$ and $(ii)$ ${\theta _0} = 49^\circ C$.
Initially,
$\frac{{(80 - 64)}}{5} = K\,\left( {\frac{{80 + 64}}{2} - {\theta _0}} \right)$ ==> $3.2 = K[72 - {\theta _0}]$ ... $(i)$
Finally
$\frac{{(64 - 52)}}{{10}} = K\,\left[ {\frac{{64 + 52}}{2} - {\theta _0}} \right]$ ==> $1.2 = K[58 - {\theta _0}]$...$(ii)$
On solving equation $(i)$ and $(ii)$ ${\theta _0} = 49^\circ C$.
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