Answer:
P = 1145.75W
λ = 4.0*10⁻²⁸m
Explanation:
Temperature T = 35°C = 308.15K
h = 1.63m
width (w) = 33.5cm = 0.335m
Length (L) = 31cm = 0.31m
Surface area of the human body =
2hw + 2hL + 2Lw
2*(1.63*0.335) + 2*(1.63*0.31) + 2*(0.31*0.335)
Area = 1.0921 + 1.0106 + 0.2077
Area = 2.3104m²
Using Stefan-Boltzmann equation,
E = εσΤ⁴
Ε = 0.97 * 5.67*10⁻⁸ * (308.15)⁴
E = 495.91 w/m²
Power = energy * surface area
Power = 495.91 * 2.3104
P = 1145.75W
b)
Applying Energy-Wavelength equation
E = hc / λ
λ = hc / E
λ = (6.626*10⁻³⁴ * 3.0⁸) / 495.91
λ = 4.0*10⁻²⁸m
Answer:
E = 1.143 KW
(λ)max = 9.4 μm = 9.4 x 10⁻⁶ m
Explanation:
a)
The total emissive power of human body can be given by Stefan-Boltzman Law:
E = AεσΤ⁴
where,
E = Total emitted power
ε = emissivity = 97% = 0.97
σ = Stefan Boltzman Constant = 5.67 x 10⁻⁸ W/m².K⁴
T = Absolute Temperature = 35°C +273 = 308 K
A = Total Surface Area of rectangular approximation = 2(1.63 m)(0.335 m) + 2(1.63 m)(0.31 m) + 2(0.335 m)(0.31 m)
A = 2.31 m²
Therefore,
E = (2.31 m²)(0.97)(5.67 x 10⁻⁸ W/m².K⁴)(308 K)⁴
E = 1143.52 W = 1.143 KW
b)
The peak wavelength or the maximum wavelength can be found out by using wein's displacement law:
[(λ)max][T] = 2.8978 x 10⁻³ m.K
(λ)max = 2897.8 μm.K/308 K
(λ)max = 9.4 μm = 9.4 x 10⁻⁶ m
