A body cools from 60,^oC to 50,^oC in 10, minutes . If room temperature is 25,^oC and assuming Newto

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10-2.Transmission of Heat

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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

$40$

C

$42.85$

D

$45$

Solution

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

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

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

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

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

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

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

Standard 11

Physics

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