First slide

Heat transfer-Radiation

Question

A liquid cools down from 70°C to 60°C in 5 minutes. The time taken to cool it from 60°C to 50°C will be

Moderate

A

5 minutes
B

Lesser than 5 minutes
C

Greater than 5 minutes
D

Lesser or greater than 5 minutes depending upon the density of the liquid

Solution

According to Newton's law of cooling,
Rate of cooling $\infty$ mean temperature difference
Initially, mean temperature difference
$= (\frac{70 + 60}{2} - θ_{0}) = (65 - θ_{0})$
Finally, mean temperature difference
$= (\frac{60 + 50}{2} - θ_{0}) = (55 - θ_{0})$
In second case, mean temperature difference decreases, so rate of fall of temperature decreases. Thus, it takes more time to cool through the same range.

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