A radiator, in a domestic heating system, operates at a temperature of 27°C. The heat
flux at the surface of a radiator, if it behaves as a black body, will be ______.
-
A.
45.927 W/m2
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B.
4.5927 W/m2
-
C.
4592.7 W/m2
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D.
459.27 W/m2
Correct Answer:
D. 459.27 W/m2
Explanation:
The heat flux emitted by a surface acting as a black body is determined by the Stefan-Boltzmann Law, which states that the total radiant energy per unit area is proportional to the fourth power of its absolute temperature.
First, convert the temperature from Celsius to Kelvin:
T = 27°C + 273.15 = 300.15 K (approximately 300 K)
Using the Stefan-Boltzmann equation:
E = σT⁴
Where σ (Stefan-Boltzmann constant) is approximately 5.67 × 10⁻⁸ W/m²·K⁴.
Calculation:
E = (5.67 × 10⁻⁸) × (300)⁴
E = (5.67 × 10⁻⁸) × (81 × 10⁸)
E = 5.67 × 81
E ≈ 459.27 W/m²
Based on this calculation, the correct heat flux is 459.27 W/m², which corresponds to option D.
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