Hot water cools from 60,^oC to 50,^oC in the first 10, min and to 42,^oC in next 10, min .&nbsp

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10-2.Transmission of Heat

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Hot water cools from $60\,^oC$ to $50\,^oC$ in the first $10\, min$ and to $42\,^oC$ in the next $10\, min$. The temperature of the surrounding is ......... $^oC$

A

$50$

B

$10$

C

$15$

D

$20$

Solution

$\frac{\theta_{1}-\theta_{2}}{t}=k\left(\frac{\theta_{1}+\theta_{2}}{2}-\theta_{0}\right)$

$\frac{60-50}{10}=k\left(\frac{60+50}{2}-\theta_{0}\right)$

$1=k\left(55-\theta_{0}\right) \dots(i)$

$\frac{60-42}{10+10}=k\left(\frac{60+42}{2}-\theta_{0}\right) \frac{18}{20}=k\left(51-\theta_{0}\right) \ldots(i i)$

Solving $(i)$ and $(i i), \theta_{0}=10^{\circ}$

Standard 11

Physics

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