Answer:
a) T = 1,932 10¹¹ K
, I = 7.90 10³⁷ W / m²
,
b) T = 1,932 10⁶ K
, I = 7.90 10¹⁷ W / m²
,
c) T = 4,528 10³ K
, I = 4.20 10⁶ W / m²
,
d) T = 2,898 10⁻³ K
, I = 4.0 10⁻¹⁰ W / m²
e) T = 1.42 10⁻⁵ K
, I= 4.07 10⁻²⁸ W / m²
Explanation:
For this exercise we can use Wien's displacement law and Stefan's law
λ T = 2,898 10⁻³
T = 2,898 10-3 / λ
P = σ A e T⁴
I = P / A = σ e T⁴
The value of the Stefan –Boltzmann (σ) constant is 5.670 10⁻⁸ W / m²K⁴, the emissivity (e) for a black body is 1
I = σ T⁴
a) λ = 1.50 10⁻¹⁴ m
The temperature is
T = 2,898 10⁻³ /λ
T = 2,898 10⁻³ / 1.50 10⁻¹⁴
T = 1,932 10¹¹ K
I = 5,670 10⁻⁸ (1,932 10¹¹)⁴
I = 7.90 10³⁷ W / m²
b) λ = 1.50 nm = 1.50 10⁻⁹ m
T = 2,898 10⁻³ / 1.50 10⁻⁹
T = 1,932 10⁶ K
I = 5,670 10⁻⁸ (1,932 10⁶)⁴
I = 7.90 10¹⁷ W / m²
c) λ = 640 nm = 6.40 10⁻⁷ m
T = 2,898 10⁻³ / 6.40 10⁻⁷
T = 4,528 10³ K
I = 5,670 10⁻⁸ (4,528 10³)⁴
I = 4.20 10⁶ W / m²
d) λ = 1.00 m
T = 2,898 10⁻³ / 1
T = 2,898 10⁻³ K
I = 5,670 10⁻⁸ (2,898 10⁻³)⁴
I = 4.0 10⁻¹⁰ W / m²
e) λ = 204 m
T = 2,898 10⁻³ / 204
T = 1.42 10⁻⁵ K
I = 5,670 10⁻⁸ (1.42 10⁻⁵)⁴
I = 4.07 10⁻²⁸ W / m²
