First slide

Radiation

Question

Certain quantity of water cools from 70⁰C to 60⁰C in the first 5 min and to 54°C in the next 5 min. The
temperature of the surrounding is

Moderate

A

45⁰C
B

20⁰C
C

42⁰C
D

10⁰C

Solution

Let temperature of surrounding be Q₀ then from Newton's law of cooling
$Case I \frac{Q_{2} - Q_{1}}{t} = K (\frac{Q_{2} + Q_{1}}{2} - Q_{0})$
$\frac{70 - 60}{5} = K (65 - Q_{0})$ …(i)
$Case II \frac{60 - 54}{5} = (57 - Q_{0}) K$ …(ii)
On dividing Eq. (i) by Eq. (ii), we get
$\frac{10}{6} = \frac{65 - Q_{0}}{57 - Q_{0}} \Rightarrow Q_{0} = 45^{\circ} C$

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