Certain quantity of water cools from 70,^oC to 60,^oC in first 10, minutes and to 54,^oC in ne

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10-2.Transmission of Heat

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Certain quantity of water cools from $70\,^oC$ to $60\,^oC$ in first $10\, minutes$ and to $54\,^oC$ in the next $10\, minutes$. The temperature of the surrounding is ......... $^oC$

A

$45$

B

$20$

C

$42$

D

$10$

Solution

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

$\frac{70-60}{10}=\mathrm{K}\left[\frac{70+60}{2}-\theta_{0}\right] \ldots .(i)$

$\frac{60-54}{10}=\mathrm{K}\left[\frac{60+54}{2}-\theta_{0}\right]$ $…(ii)$

$\frac{10}{6}=\frac{65-\theta_{0}}{57-\theta_{0}}$

solving it $\theta_{0}=45^{\circ} \mathrm{C}$

Standard 11

Physics

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