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  • A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C.How long it will take to cool from 75°C to 69°C?<div class='qna-optio

A bowl filled with very hot soup cools from 98°C to 86°C in 2 minutes when the room temperature is 22°C.How long it will take to cool from 75°C to 69°C?

Option: 1

1 minute


Option: 2

1.4 minutes


Option: 3

0.5 minute


Option: 4

2 minutes


Answers (1)

best_answer

According to NLC,
\begin{aligned} & -\frac{\mathrm{d} \theta}{\mathrm{dt}}=\mathrm{k} \theta \\ & \frac{12}{2}=\mathrm{K}\left(\frac{98+86}{2}-22\right) \\ & \Rightarrow 6=\mathrm{K}(92-22)=\mathrm{K} \times 70 \\ & \Rightarrow \mathrm{K}=\frac{6}{70} \end{aligned}...(i)
Now, \frac{6}{t_2}=\frac{6}{70}\left(\frac{75+69}{2}-22\right)
\begin{aligned} & =\frac{6}{70} \times(72-22) \\ & \mathrm{t}_2=\frac{6 \times 70}{6 \times 50} \\ & \frac{7}{5}=1.4 \mathrm{~min} \end{aligned}

Posted by

jitender.kumar

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