First slide

Heat transfer-Radiation

Question

A body initially at 80°C cools to 64°C in 5 minutes and to 52°C in 10 minutes. The temperature of the body after 15 minutes will be

Moderate

A

42.7°C
B

35°C
C

47°C
D

40°C

Solution

According to Newton's law of cooling,
$\frac{θ_{1} - θ_{2}}{t} = K [\frac{θ_{1} + θ_{2}}{2} - θ_{0}]$

For first process: $\frac{(80 - 64)}{5} = K [\frac{80 + 64}{2} - θ_{0}]$ …(i)
For second process: $\frac{(80 - 52)}{10} = K [\frac{80 + 52}{2} - θ_{0}]$ …(ii)
For third process: $\frac{(80 - θ)}{15} = K [\frac{80 + θ}{2} - θ_{0}]$ …(iii)
On solving Eqs. (i) and (ii), we get
$K = \frac{1}{15} and θ_{0} = 24^{\circ} C$
Putting these values in Eq. (iii), we get
$θ = 42 {.7}^{\circ} C$
.

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