First slide

Radiation

Question

A body is heated to $327^{o} C$ and then allowed to cool in air which is at $27^{o} C$ . Initial rate of cooling of the body is R. What will be the rate of cooling of the body when its temperature falls to $227^{o} C$ ?

Easy

A

0.447 R
B

0.565 R
C

0.821 R
D

0.325 R

Solution

Rate of cooling, $R \propto (T^{4} - T_{0}^{4})$
$∴ \frac{R^{1}}{R} = \frac{{(227 + 273)}^{4} - {(27 + 273)}^{4}}{{(327 + 273)}^{4} - {(27 + 273)}^{4}} = \frac{625 - 81}{1296 - 81}$
$\Rightarrow R^{1} = R \times \frac{544}{1215} = 0.447 R$

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