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  • A cup of coffee cools from in t minutes, when the room temperature is <im

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:

 

Option: 1

\frac{13}{10}t


Option: 2

\frac{13}{5 }t


Option: 3

\frac{10}{13 }t

 


Option: 4

\frac{5}{13}t


Answers (1)

best_answer

\frac{\Delta T}{\Delta t}=-k \left ( T_{ang}-T_0 \right )

\frac{\frac{90-80}{t}}{\frac{(80-60)}{\Delta t}}=\frac{\left(\frac{90+80}{2}-20\right)}{\left(\frac{80+60}{2}-20\right)}

\frac{\frac{10}{t}}{\frac{20}{\Delta t}}=\frac{65}{50}=\frac{13}{10}

\frac{\Delta t}{2t}=\frac{13}{10}

\Delta t=\frac{13\;t}{5}

Posted by

Irshad Anwar

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