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The temperature of a solid surface changes from 27 K to 627 K. The emissive power changes would then confirm to the ratio
  • a)
    6:1
  • b)
    9:1
  • c)
    81:1
  • d)
    27:1
Correct answer is option 'C'. Can you explain this answer?
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The temperature of a solid surface changes from 27 K to 627 K. The emi...
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The temperature of a solid surface changes from 27 K to 627 K. The emi...
Explanation:

Given:
Initial temperature (T1) = 27 K
Final temperature (T2) = 627 K

Concept:
According to the Stefan-Boltzmann law, the emissive power (P) of a surface is directly proportional to the fourth power of its absolute temperature. Mathematically, it can be expressed as:

P ∝ T^4

Where P is the emissive power and T is the absolute temperature.

Calculation:
To calculate the change in emissive power, we need to calculate the ratio of the emissive powers at the final and initial temperatures.

Let's calculate the emissive powers at the initial and final temperatures:

P1 = T1^4
P2 = T2^4

Substituting the given values:

P1 = (27 K)^4
P2 = (627 K)^4

P1 = 531,441 K^4
P2 = 742,765,625 K^4

Now, calculate the ratio of the emissive powers:

Ratio = P2 / P1
= 742,765,625 K^4 / 531,441 K^4
= 81

Hence, the ratio of the emissive powers is 81:1.

Therefore, the correct answer is option 'C' (81:1).
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