# Homework Help: Black Body Radiation

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1. Mar 19, 2016

### mukul

1. The problem statement, all variables and given/known data

In a dark room with ambient temperature T0, a black body is kept at a temperature T. Keeping the temperature of the black body constant (at T), sunrays are allowed to fall on the black body through a hole in the roof of the dark room. Assuming that there is no change in the ambient temperature of the room, which of the following statement(s) is/are correct?

(A) The quantity of radiation absorbed by the black body in unit time will increase.
(B) Since emissivity = absorptivity, hence the quantity of radiation emitted by black body in unit time will
increase.
(C) Black body radiates more energy in unit time in the visible spectrum.
(D) The reflected energy in unit time by the black body remains same.

2. Relevant equations

emissivity=absorptivity

3. The attempt at a solution

I think A and D are correct

A) After opening the hole in the roof greater amount of heat is falling on the black body so it will absorb greater amount of heat;
B) Radiations emitted by black body just depends on temperature of black body, so there will be no change in radiation emitted.
C) Again since radiation spectra of black body just depends on temperature of black body so there will be no change in radiation spectra of black body
D) Black body do not reflect anything so there will be no change in radiations reflected

But the answer given in various books is A,B,C,D unanimously.

A) This website tries to explain it. http://www.madsci.org/posts/archives/2009-02/1235742866.Ph.r.html

Last edited: Mar 19, 2016
2. Mar 19, 2016

### drvrm

-seems to be true.

however it will be difficult to maintain the temperature T2 and T1

i have some doubt regarding above as i have not seen/can visualize black body as a reflector.
for others the following may be used.
For a body of any arbitrary material emitting and absorbing thermal electromagnetic radiation at every wavelength in thermodynamic equilibrium, the ratio of its emissive power to its dimensionless coefficient of absorption is equal to a universal function only of radiative wavelength and temperature. That universal function describes the perfect black-body emissive power.
For an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.
i could not get the purpose behind the experimental set-up.

3. Mar 19, 2016

### mukul

Is it safe to assume that according to you, following is the status
A correct
B incorrect
C incorrect
D not sure

4. Mar 19, 2016

### SammyS

Staff Emeritus
Regarding (D):

An ideal black body absorbs all incident electromagnetic radiation.

5. Mar 19, 2016

### drvrm

i think my answer is (taking the thought experiment of maintaining the black body at a constant temp as well as the room temp also constant through out the measurement)
A. incorrect-radiation absorbed per unit time will be constant-that constant value may change after exposure to sunlight
B. incorrect-quantity of radiation emitted by black body in unit time will remain constant (a raised value of new constant)
C. incorrect
D. Correct(If we take reflectivity to be zero)

6. Mar 19, 2016

### SammyS

Staff Emeritus
I would say the first three are correct .

7. Mar 19, 2016

### mukul

SammyS can you please explain how did arrive at that. Specially parts B and C

8. Mar 19, 2016

### SammyS

Staff Emeritus
I should have said: "Your answers are correct for the first three."