Wavelength associated with maximum spectral emissive power of two black spheres A and B are 11 and 12 respectively. Radius of sphere A and B are ra and rp and both spheres are made by same material. Both spheres are kept in surrounding of temperature of O K. If ratio of initial rate of 60 cooling of sphere A and B is then value of 12 nis. (Given: V2 ) ГА 21 n 'B -3; = =
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Answer:
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Answer:
The value of 12 nis is equal to (60/12) * (T4B - T4A).
Explanation:
From the above question,
They have given :
The wavelength associated with the maximum spectral emissive power of two black spheres, A and B, is 11 and 12, respectively.
The radius of sphere A and B are ra and rp and both spheres are made of the same material. Both spheres are kept in a surrounding temperature of 0 K. The initial rate of cooling of sphere A and B is 60 nis, and the ratio of the two is given by V2/V1.
By calculating the Stefan-Boltzmann Law, we can determine that the total rate of cooling for each sphere is given by:
Sphere A: R1 = σT4A4πra2
Sphere B: R2 = σT4B4πrb2
Where σ is the Stefan-Boltzmann Constant and T is the temperature of the surrounding environment. We can then solve for the temperature of the spheres in order to calculate their cooling rates:
Sphere A: T4A = (R1/(σ4πra2))
Sphere B: T4B = (R2/(σ4πrb2))
Finally,
We can use the ratio of the initial cooling rates and the temperatures of the two spheres to calculate the value of 12 nis:
Value of 12 nis = (R1/R2) * (T4B - T4A)
Thus, the value of 12 nis is equal to (60/12) * (T4B - T4A).
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