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6 April, 15:09

Two objects of the same size are both perfect blackbodies. One has a temperature of 3000 K, so its frequency of maximum emission is in the infrared region of the spectrum. The other has a temperature of 12,000 K, so its frequency of maximum emission is in the ultraviolet region of the spectrum.

Compared to the object at 3000 K, the object at 12,000 K:

A. emits more light in the infrared region of the spectrum.

B. emits more light in the visible region of the spectrum.

C. emits more light in the ultraviolet region of the spectrum

D. emits more light in only two of the three listed spectral regions.

E. emits more light in all three spectral regions.

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  1. 6 April, 17:03
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    a) The colder body (3000k), b) hearter body c) 12000K body

    Explanation:

    This exercise should know the power emitted by the objects and the distribution of this emission in the energy spectrum, for this we will use Stefan's laws and that of Wien's displacement

    Stefan's Law P = σ A e T⁴

    Wien displacement law λ T = 2,898 10⁻³ m K

    Let's calculate the power emitted for each object.

    As they are perfect black bodies e = 1, they also indicate that they have the same area

    T = 3000K

    P₁ = σ A T₁⁴

    T = 12000K

    P₂ = σ A T₂⁴

    P₂ / P₁ = T₂⁴ / T₁⁴

    P₂ / P₁ = (12000/3000) ⁴

    P₂ / P₁ = 256

    This indicates that the hottest body emission is 256 times the coldest body emission.

    Let's calculate the maximum emission wavelength

    Body 1

    T = 3000K

    λ T = 2,898 10-3

    λ₁ = 2.89810-3 / T

    λ₁ = 2,898 10-3 / 3000

    λ₁ = 0.966 10-6 m

    λ₁ = 966 nm

    T = 12000K

    λ₂ = 2,898 10-3 / 12000

    λ₂ = 0.2415 10-6 m

    λ₂ = 214 nm

    a) The colder body (3000k) emits more light in the infrared, since the emission of the hot body is at a minimum (emission tail)

    b) The two bodies have emission in this region, the body of 3000K in the part of rise of the emission and the body to 12000K in the descent of the emission even when this body emits 256 times more than the other, so this body should have the highest broadcast in this area

    c) The emission of the hottest 12000K body is mainly in UV

    d) The hottest body emits more energy in UV and visible

    e) No body has greater emission in all zones
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