The temperatures of two bodies \(A\) and \(B\) are respectively 727\(^\circ\)C and 327\(^\circ\)C. The ratio \(H_A : H_B\) of the rates of heat radiated by them is
Show Hint
- 727 : 327
- 5 : 3
- 25 : 9
- 625 : 81
The Correct Option is D
Solution and Explanation
By Stefan's law: \(H \propto T^4\) (in Kelvin).
Step 2: Detailed Explanation:
\(T_A = 727 + 273 = 1000\) K, \(T_B = 327 + 273 = 600\) K
\[ \frac{H_A}{H_B} = \left(\frac{T_A}{T_B}\right)^4 = \left(\frac{1000}{600}\right)^4 = \left(\frac{5}{3}\right)^4 = \frac{625}{81} \]
Step 3: Final Answer:
\(H_A : H_B = 625 : 81\).
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