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  4. A cup of coffee cools from 90° C to 80° C in t minutes, when the room temperature is 20° C. The time taken by a similar cup of coffee to cool from 80° C to 60° C at a room temperature same at 20° C is :

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Q. A cup of coffee cools from $90^{\circ} C$ to $80^{\circ} C$ in t minutes, when the room temperature is $20^{\circ} C$. The time taken by a similar cup of coffee to cool from $80^{\circ} C$ to $60^{\circ} C$ at a room temperature same at $20^{\circ} C$ is :

NEETNEET 2021Thermodynamics

Solution:

$\frac{\left(\frac{80-60}{t'}\right)}{\left(\frac{90-80}{t}\right)}=\frac{\left(\frac{80+60}{2}-20\right)}{\left(\frac{90+80}{2}-20\right)}$
$\Rightarrow \frac{20}{t'} \times \frac{t}{10}=\frac{50}{65} $
$\Rightarrow t=2 t \times \frac{65}{50}=\frac{13}{5} t$