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7 Common Problems of Black Body Radiation

physics.fisikastudycenter.com,-Learning black body radiation in the common problems and answers, wien displacement law and stefan-boltzmann law will be involved in the discussions.

Problem 1
A body has its minimum and maximum temperatures respectively 27oC and 227oC.
Find the ratio of radiated power at its maximum and minimum temperatures!

Answer
Data :
T1 = 27oC = 300 K
T2 = 227oC = 500 K
P2/P1 = (T2/T1)4
P2/P1 = (500/300)4 = (5/3)4 = 625 : 81

Problem 2
A body with area surface of 100 cm2 and temperature of 727oC. If Stefan-Boltzman 5,67 x 10−8 W/mK4 and the body emisivity is 0,6 determine the average of radiated energy of the body!

Answer
Data :
σ = 5,67 x 10−8 W/mK4
T = 727oC = 1000 K
e = 0,6
A = 100 cm2 = 100 x 10−4 = 10−2

So then :
P = eσ T 4A
P = (0,6)(5,67 x 10−8 )(1000)4(10−2)
P = 340,2 joule/s

Problem 3
The radiated power of a body at 227oC is 1200 J/s. If the temperature then is raised to i 727oC, find the radiated power of the body now!

Answer
Data :
T1 = 227oC = 500 K
T2 = 727oC = 1000 K
P1 = 1200 watt
So then:
P2/P1 = (T2/T1)4
P2/P1 = (1000/500)4
P2 = (1000/500)4 x P1
P2 = (2)4 x 1200 = 16 x 1200 = 19200 watt

Problem 4
A body surface at 37oC radiates an electromagnetic wave. If Wien constant is 2,898 x 10−3 m.K find the peak of wavelength radiated!
A. 8,898 x 10−6 m
B. 9,348 x 10−6 m
C. 9,752 x 10−6 m
D. 10,222 x 10−6 m
E. 11,212 x 10−6 m

Answer
Data :
T = 37oC = 310 K
C = 2,898 x 10−3 m.K
λm = ....?

λm T = C
λm (310) = 2,898 x 10−3
λm = 9,348 x 10−6 m

 

Problem 5
Graph show the relationship between intensity (I) and peak wavelength (λm) radiated of a blackbody.



If Wien constant is 2,9 x 10−3 mK, find the peak wavelength radiated at T1 !
A. 5.000 Å
B. 10.000 Å
C. 14.500 Å
D. 20.000 Å
E. 25.000 Å

Answer
Data :
T = 1727oC = 2000 K
C = 2,9 x 10−3 m.K
λmaks = ....?

λmaks T = C
λmaks (2000) = 2,9 x 10−3
λmaks = 1,45 x 10−6 m = 14.500 Å

Problem 6
The peak wavelength radiated of a body at a temperature of T Kelvin is 6000 Å. When the temperature is raised to 3/2 T Kelvin , find the new peak wavelength of the body

Answer
Data :
T1 = T Kelvin
T2 = 3/2 T Kelvin
λm 1 = 6000 Å
λm 2 = ....?

λm2 T2 = λm 1 T1
λm 2 (3/2 T) = 6000 Å (T)
λm 2 = (2/3) x 6000 Å = 4000 Å

Problem 7
A blocbody at a temperature of T Kelvin radiates 300 mW of power. Find the power radiated at temperature of ½ T Kelvin!
(A) 300 mW
(B) 150 mW
(C) 75 mW
(D) 37,5 mW
(E) 18,75 mw

Try...,!

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