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The total emissive power of a surface is 500 W/ m2 at temperature T1 and 1200 W/m2 at emperature T2, where the temperature are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperature T1/T2 is
[2015]
  • a)
    0.0308
  • b)
    0.416
  • c)
    0.803
  • d)
    0.874
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The total emissive power of a surface is 500 W/ m2 at temperature T1 a...
Emissive power ∝ T4
⇒ 
∴ 
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Most Upvoted Answer
The total emissive power of a surface is 500 W/ m2 at temperature T1 a...
Given:
Emissive power at temperature T1 = 500 W/m2
Emissive power at temperature T2 = 1200 W/m2

Assumption: Emissivity of the surface is constant.

To calculate: T1/T2

Formula: Emissive power (P) = emissivity (ε) × Stefan-Boltzmann constant (σ) × T^4
where σ = 5.67 × 10^-8 W/m2K^4

Calculation:
P1 = εσT1^4
P2 = εσT2^4

Dividing P1 by P2, we get:
P1/P2 = T1^4/T2^4

Given P1 = 500 W/m2 and P2 = 1200 W/m2
500/1200 = T1^4/T2^4
T1/T2 = (500/1200)^(1/4)

T1/T2 = 0.8028 ≈ 0.803

Therefore, the ratio of T1/T2 is 0.803 or option (c).

Note: The Stefan-Boltzmann constant is a physical constant that relates the temperature of a surface to the amount of thermal radiation it emits. The emissivity of a surface is a measure of its ability to emit thermal radiation.
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The total emissive power of a surface is 500 W/ m2 at temperature T1 and 1200 W/m2 at emperature T2, where the temperature are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperature T1/T2 is[2015]a)0.0308b)0.416c)0.803d)0.874Correct answer is option 'C'. Can you explain this answer?
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