First slide

Radiation

Question

Certain quantity of water cools from 70⁰C to 60⁰C in the first 5 minutes and to 54⁰C in the next 5 minutes. The temperature of the surroundings is

Easy

A

20⁰C
B

42⁰C
C

10⁰C
D

45⁰C

Solution

According to Newton's Law of cooling, $\large \frac {\theta_1-\theta_2}{t}\propto (\theta-\theta_0)\;where\;\theta=\frac {\theta_1+\theta_2}{2}$
$\large \frac {\theta_1-\theta_2}{t}=k\left [ \frac {\theta_1+\theta_2}{2}-\theta_0 \right ]$
$\large \frac {70-60}{5}=k\left [ \frac {70+60}{2} -\theta_0\right ]........(i)$
$\large \frac {60-54}{5}=k\left [ \frac {60+54}{2} -\theta_0\right ]........(ii)$
$\large (i)/(ii)\Rightarrow \frac {10}{6}=\frac {65-\theta_0}{57-\theta_0},\theta_0=45^0C$

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