First slide

Convection

Question

A body cool from 90°C to 70°C in 10 minutes if temperature of surrounding is 20°C find the time taken by body to cool from 60 °C to 30 °C. Assuming Newton's law of cooling is
valid:

Moderate

A

10 min
B

24 min
C

36 min
D

8 min

Solution

By Newton's law of cooling
$\frac{θ_{1} - θ_{2}}{t} = k [\frac{θ_{1} + θ_{2}}{2} - θ_{0}] \Rightarrow \frac{90 - 70}{10} = k [\frac{90 + 70}{2} - 20] and \frac{60 - 30}{t} = k [\frac{60 + 30}{2} - 20] \Rightarrow \frac{20 t}{10 \times 30} = \frac{60}{25} \Rightarrow t = 36 \min .$

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