A) \[\frac{H}{16}\]
B) \[\left( \frac{9}{27} \right)H\]
C) \[\left( \frac{16}{3} \right)H\]
D) \[\left( \frac{3}{16} \right)H\]
Correct Answer: D
Solution :
From Stefans law, the total radiant energy emitted per second per unit surface area of a black body is proportional to the fourth power of the absolute temperature of the body. That is \[E=\sigma {{T}^{4}}\] where, \[\sigma \]is Stefans constant. When sphere cools from 600 K to 200 K, energy 400 K to 200 K then. \[H=\sigma [{{(600)}^{4}}-{{(400)}^{4}}]\] \[\frac{H}{H}=\frac{[{{(600)}^{4}}-{{(200)}^{4}}]}{[{{(600)}^{4}}-{{(400)}^{4}}]}\] Using\[{{a}^{4}}-{{b}^{4}}=({{a}^{2}}-{{b}^{2}})({{a}^{2}}+{{b}^{2}}),\]we have \[\frac{H}{H}=\frac{[{{(600)}^{2}}-{{(200)}^{2}}]}{[{{(600)}^{2}}-{{(400)}^{2}}]}\times \frac{[{{(600)}^{2}}+{{(200)}^{2}}]}{[{{(600)}^{2}}+{{(400)}^{2}}]}\] \[\frac{H}{H}=\frac{32}{12}\times \frac{40}{20}=\frac{16}{3}\] \[H=\frac{3}{16}H\]
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