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10-2.Transmission of Heat
hard
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 ...... $^oC$
A
$26$
B
$49$
C
$35$
D
$42$
Solution
(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 $(ii)$ ${\theta _0} = 49^\circ C$.
Standard 11
Physics
