A body takes $5$ minute to cool from $80°C$ to $50°C$ . ...... $\min.$ it will take to cool from $60°C$ to $30°C$ , if room temperature is $20°C$ .
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(b) According to Newton’s law of cooling
in first case,$\frac{{80 - 50}}{5} = K\left[ {\frac{{80 + 50}}{2} - 20} \right]$…..$(i)$
in second case,$\frac{{60 - 30}}{t} = k\left[ {\frac{{60 + 30}}{2} - 20} \right]$ $(ii)$
Dividing equation $(i)$ by $(ii)$ we get, $\frac{t}{2} = \frac{{45}}{{25}}$==>$t = 9$min.
in first case,$\frac{{80 - 50}}{5} = K\left[ {\frac{{80 + 50}}{2} - 20} \right]$…..$(i)$
in second case,$\frac{{60 - 30}}{t} = k\left[ {\frac{{60 + 30}}{2} - 20} \right]$ $(ii)$
Dividing equation $(i)$ by $(ii)$ we get, $\frac{t}{2} = \frac{{45}}{{25}}$==>$t = 9$min.
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