A body cools from 60 ,^oC to 50 ,^oC in 10 ,minutes . If the room… - Vidyadip

MCQ

A body cools from $60\,^oC$ to $50\,^oC$ in $10\,minutes$ . If the room temperature is $25\,^oC$ and assuming Newton's law of cooling to hold good, the temperature of the body at the end of the next $10\,minutes$ will be ......... $^oC$

A
$38.5$
B
$40$
✓
$42.85$
D
$45$

✓

Answer

Correct option: C.

$42.85$

c
$\frac{\theta_{1}-\theta_{2}}{t}=\left[\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right] K$

$\frac{60-50}{10}=\mathrm{K}[55-25]$

$K=\frac{1}{30}$

$\frac{50-\theta_{1}}{10}=\frac{1}{30}\left[\frac{\theta_{1}+50}{2}-25\right]$

$6\left[50-\theta_{1}\right]=\theta_{1}$

$\Rightarrow 7 \theta_{1}=300$

$\Rightarrow \theta_{1}=\frac{300}{7}$

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