First slide

Heat transfer-Radiation

Question

A body cools down from 60°C to 55°C in 30 s. Using Newton’s law of cooling, calculate the approximate time taken by same body to cool down from 5 5°C
to 50°C. Assume that the temperature of surroundings is 45°C.

Moderate

Solution

According to Newton’s law of cooling
$\frac{θ_{1} - θ_{2}}{t} = K [\frac{θ_{1} + θ_{2}}{2} - θ_{0}]$
$\frac{60 - 55}{30} = K [\frac{60 + 55}{2} - 45]$ ……………(i)
Similarly, for 2nd case,
$\frac{55 - 50}{t} = K [\frac{55 + 50}{2} - 45]$ ……………(ii)
Dividing Eq. (i) by Eq. (ii), we get, t = 50

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