A black body calorimeter filled with hot water cools from 60^o C to 50^o C in 4 ,,min and 40^o C to

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10-2.Transmission of Heat

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A black body calorimeter filled with hot water cools from $60^o C$ to $50^o C$ in $4 \,\,min$ and $40^o C$ to $30^o C$ in $8 \,\min$. The approximate temperature of surrounding is ........ $^oC$

A

$10$

B

$15$

C

$20$

D

$25$

Solution

Assuming the temperature of surrounding be $t^{o} C$

$CASE-1$

$\frac{(60-50)}{4 \min }=k(55-t)$ $(1)$

Again, $CASE- 2$

$\frac{(40-30)}{8 \min }=k(35-t)$ $(2)$

$\frac{(1)}{(2)}=\frac{\frac{10}{4}}{\frac{10}{8}}=\frac{(55-t)}{(35-t)}$

$\Rightarrow 2(35-t)=55-t$

$\Rightarrow 70-2 t=55-t$

$\Rightarrow t=15^{\circ} \mathrm{C}$

Standard 11

Physics

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