# Solving the Steffan-Boltzman Law: Transfer of Power from Left to Right Plate

• shyta
In summary: It would really help if you explained in detail how much you do understand. Which parts did you work out yourself, and which parts have you simply copied from somewhere else? Please show your own work more clearly. Explain with more detail exactly what it is that you don't understand. And is this part of a homework question?It is not part of a homework question.
shyta
Hi guys, I need help on my concept on the steffan's law.

I understand that for a grey body sphere confined within a blackbody spherical shell, the general forumla for the net power radiated from inner sphere should be

where k=stefan boltzman's constant

However recently, I was given a question which made me really confused.
For the case where 2 plates are separated by a gap and the left plate has a higher temp, T1 and emissivity, e1 = 1, as compared to the right plate having T2 and emissivity e2. Then the net rate of power transferred from the left to the right is?

Prad by left plate = kAe1T14
Prad by right plate = kAe2T24
which all of it is absorbed by the left plate since emissivity is 1

then fraction absorbed by right plate is e2
and fraction reflected by right plate is 1-e2(all absorbed by the left plate)

Pnet flow from left to right = kA (e1T14e2 - e2T24)

But how??

anyone? :(

shyta said:
Pnet flow from left to right = kA (e1T14e2 - e2T24)

But how??

I agree, net power transfer is $Ake_2(T_1^4-T_2^4)$. What's the problem?

why is it e_2 and not e_1?

Why is which e_2? Why wouldn't it be e_2?
It would really help if you explained in detail how much you do understand. Which parts did you work out yourself, and which parts have you simply copied from somewhere else? Please show your own work more clearly. Explain with more detail exactly what it is that you don't understand. And is this part of a homework question?

No it's not part of a homework.

isn't the emissivity used supposed to be the one of the object, as in for the 2 plates situation, the emissivity of the left plate (e=1?)

what i am confused about is why there is a need to multiply by the fraction absorbed by the right plate when finding the net transfer?

If you want my help, it would be great if you helped me more to help you. Are you saying that you yourself figured out everything except the second last line of your original post, but that second last line you took from a book and do not know how to obtain yourself?

Some components to consider:
- the radiation from 2 to 1.
- the fraction of the radiation from 1 that is absorbed by 2.
Note these are in opposite directions. Do you know how to combine these into the "net"?

Alternatively:
- the initial radiation from 2, in one direction.
- all the radiation from 1, in the other direction.
- the part, of the radiation originally from 1, that reflects back from 2 to 1 again, in the first direction.
This should also give the same answer.

yes i did take it from something like a book.

Prad by left plate = kAe1(T14-T24)

then we have to consider the fraction reflected by the right plate which got absorbed back by the left plate which is 1-e2

which is the part I'm confused about

What is "like a book"? Please cite your source.

What does "Prad" mean?

Can you calculate exactly how much power, in Watts, the right plate absorbs? (And exactly how much power reflects back at the left plate?)

Is it easier to solve the problem if I choose e_2 = 0.25 ?

## 1. What is the Steffan-Boltzman Law?

The Steffan-Boltzman Law is a physical law that describes the relationship between the temperature of an object and the amount of thermal radiation it emits. It states that the total power radiated per unit surface area of an object is proportional to the fourth power of its absolute temperature.

## 2. How does the Steffan-Boltzman Law relate to heat transfer?

The Steffan-Boltzman Law is used to calculate the transfer of heat energy from one object to another. It states that the rate of heat transfer between two objects is directly proportional to the difference in their temperatures and the surface area of the objects, and is also affected by the emissivity of the objects' surfaces.

## 3. What is meant by the "left to right plate" in the context of the Steffan-Boltzman Law?

The "left to right plate" refers to a hypothetical situation in which there are two parallel plates with different temperatures, and heat energy is transferred between them. The left plate is typically considered to be at a higher temperature, while the right plate is at a lower temperature.

## 4. How is the transfer of power calculated in the Steffan-Boltzman Law?

The transfer of power, or heat flux, is calculated using the formula Q = σε(TL4 - TR4), where Q is the heat flux, σ is the Stefan-Boltzman constant, ε is the emissivity of the object's surface, and TL and TR are the temperatures of the left and right plates, respectively.

## 5. What are some practical applications of the Steffan-Boltzman Law?

The Steffan-Boltzman Law has many practical applications in engineering and physics, including the design of heat transfer systems, such as radiators and heat exchangers. It is also used in the study of planetary atmospheres and the transfer of heat energy in stars. Additionally, the law is applied in the development of infrared cameras and other thermal imaging devices.

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