Hot water cools from 60,^oC to 50,^oC in first 10,minutes and to 42,^oC in next 10,minutes . tempera

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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 $10\,minutes$ and to $42\,^oC$ in the next $10\,minutes$. The temperature of the surroundings is ......... $^oC$

A

$30$

B

$20$

C

$15$

D

$25$

Solution

$\frac{\mathrm{T}_{1}-\mathrm{T}_{2}}{\mathrm{t}}=\mathrm{K}\left(\frac{\mathrm{T}_{1}+\mathrm{T}_{2}}{2}-\mathrm{T}_{0}\right)$

$\frac{60-50}{10}=\mathrm{K}\left(55-\mathrm{T}_{0}\right)$

$1=\mathrm{K}\left(50-\mathrm{T}_{0}\right)$ $…(1)$

$\frac{50-42}{10}=\mathrm{K}\left(\frac{50-42}{2}-\mathrm{T}_{0}\right)$

$\frac{8}{10}=\mathrm{K}\left(46-\mathrm{T}_{0}\right)$ $….(2)$

$\operatorname{eqn}(2) \div \operatorname{eqn}(1)$

$\frac{8}{10}=\frac{46-\mathrm{T}_{0}}{50-\mathrm{T}_{0}}$

$400-8 T_{0}=460-10 T_{0}$

$2 \mathrm{T}_{0}=60 \Rightarrow \mathrm{T}_{0}=30^{\circ} \mathrm{C}$

Standard 11

Physics

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