First slide

Heat transfer-Radiation

Question

A bucket fulI of hot water cools from 75^oC to 70^oC in time T₁, from 70^oC to 65^oC in time T₂ and from 65^oC to 60^oC in time T₃, then

Moderate

A

$T_{1} = T_{2} = T_{3}$
B

$T_{1} > T_{2} > T_{3}$
C

$T_{1} < T_{2} < T_{3}$
D

$T_{1} > T_{2} < T_{3}$

Solution

According to Newton's law of cooling
Rate of cooling $\propto$ Mean temperature difference
$\begin{array}{l} \Rightarrow \frac{Fall in temperature}{Time} \propto (\frac{θ_{1} + θ_{2}}{2} - θ_{0}) \\ ∵ {(\frac{θ_{1} + θ_{2}}{2})}_{1} > {(\frac{θ_{1} + θ_{2}}{2})}_{2} > {(\frac{θ_{1} + θ_{2}}{2})}_{3} \end{array}$
$\Rightarrow T_{1} < T_{2} < T_{3}$

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