An object is cooled from $75°C$ to $65°C$ in $2$ minutes in a room at $30°C$ . The time taken to cool another object from $55°C$ to $45°C$ in the same room in minutes is
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(a) According to Newton’s law of cooling
in first case, $\frac{{75 - 65}}{t} = K\left[ {\frac{{75 + 65}}{2} - 30} \right]$…..$(i)$
in second case,$\frac{{55 - 45}}{t} = K\left[ {\frac{{55 + 45}}{2} - 30} \right]$…..$(ii)$
Dividing eq. $(i)$ by $(ii)$ we get $\frac{{5t}}{{10}} = \frac{{40}}{{20}}$==>$t = 4$minutes
in first case, $\frac{{75 - 65}}{t} = K\left[ {\frac{{75 + 65}}{2} - 30} \right]$…..$(i)$
in second case,$\frac{{55 - 45}}{t} = K\left[ {\frac{{55 + 45}}{2} - 30} \right]$…..$(ii)$
Dividing eq. $(i)$ by $(ii)$ we get $\frac{{5t}}{{10}} = \frac{{40}}{{20}}$==>$t = 4$minutes
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