First slide

Convection

Question

Certain quantity of water cools from 70°C to 60°C in the first 5 minutes and to 54 °C in the next 5 minutes. The temperature of the surroundings is:

Easy

A

45°C
B

20°C
C

42°C
D

10°C

Solution

By newton's law of cooling
$\frac{θ_{1} - θ_{2}}{t} = k [\frac{θ_{1} + θ_{2}}{2} - θ_{0}] \Rightarrow \frac{70 - 60}{5} = k [\frac{70 + 60}{2} - θ_{0}] \Rightarrow 2 = k [65 - θ_{0}] . . (i) and \frac{60 - 54}{5} = k [\frac{60 + 54}{2} - θ_{0}] \Rightarrow \frac{6}{5} = k [57 - θ_{0}] . . (ii)$
By dividing eqn.(i) by eqn.(ii) we have
$\frac{10}{6} = \frac{65 - θ_{0}}{57 - θ_{0}} \Rightarrow θ_{0} = 45^{o}$

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