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10-2.Transmission of Heat
easy
A liquid cools down from ${70^o}C$ to ${60^o}C$ in $5$ minutes. The time taken to cool it from ${60^o}C$ to ${50^o}C$ will be
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
(c) According to Newton's law of cooling
Rate of cooling ? mean temperature difference.
Initially, mean temperature difference $ = \left( {\frac{{70 + 60}}{2} – {\theta _0}} \right) = (65 – {\theta _0})$
Finally, mean temperature difference $ = \left( {\frac{{60 + 50}}{2} – {\theta _0}} \right) = (55 – {\theta _0})$
In second case mean temperature difference decreases, so rate of fall of temperature decreases, so it takes more time to cool through the same range.
Standard 11
Physics