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1. Jul 25, 2015

### PytrTchaikovsky

Dear forum

I am working with thermal radiation. This is the specific formula:
P = σ ⋅ A ⋅ T4
P = emitted effect (W, J/s)
σ = Stefan-Boltzmann constant (5,67 ⋅ 10-8)
A = area of object (m2)
T = temperature of object (K)

How can I get to know the total emitted joules, within a certain range of temperature? Any formula out there? I think this is a tricky one because the more joules emitted, the less joules is being emitted (because temperature is lowered), if you know what I mean.

Best regards

2. Jul 25, 2015

### Qwertywerty

Is there some reason you think it isn't simply M*c*ΔT ?

Last edited: Jul 25, 2015
3. Jul 25, 2015

### PytrTchaikovsky

Where M is thermal emittance? And c is specific heat?

If M is thermal emittance, which thermal emittance? Since it is changing?

Thank you

4. Jul 25, 2015

### Qwertywerty

M is mass of object ( Q = mcΔT ) .

5. Jul 25, 2015

### gleem

From your initial equation you can write dP =4σA T3dt giving the power in the interval dt

6. Jul 25, 2015

### Staff: Mentor

Under what conditions? Radiating into vacuum, with no absorption?

Also, why would you want it within a certain range of temperature?

7. Jul 25, 2015

### Qwertywerty

Why would you need vacuum for no absorption ? A body could be placed with another body in vacuum too - the OP's first post only mentions power emitted .

I didn't understand what was wrong with asking this .

8. Jul 25, 2015

### Staff: Mentor

If there are other objects present, they will also be emitting radiation, so the object the OP is asking about will be absorbing radiation as well as emitting it. That wil affect its temperature.

I was just trying to understand the scenario the OP had in mind. Normally when people ask about total energy emitted by an object, they ask about energy emitted over some period of time, not over some range of temperature.

9. Jul 25, 2015

### Staff: Mentor

This gives the rate of change of power with respect to time, i.e., the change in power in the interval dt. It does not give the power itself.

10. Jul 25, 2015

### Qwertywerty

Post edited .

Last edited: Jul 25, 2015
11. Jul 25, 2015

### Qwertywerty

Wouldn't it still remain m*c*ΔT if temperature of surroundings remain the same ?

Last edited: Jul 25, 2015
12. Jul 25, 2015

### Qwertywerty

But there could be other objects in vacuum too .

13. Jul 26, 2015

### nasu

It's not wrong to ask but the question is not well defined.
You have in mind a body with a distribution of temperatures? Or a body whose temperature changes in time? Or maybe something else?

I am puzzled by how many people jump with answers before trying to figure out what the question is. :)
I am not referring to this thread in particular.

14. Jul 26, 2015

### PytrTchaikovsky

Sorry for being unclear, thought I should make this as general as possible but I'll be more specific. I want to calculate the total amount of joules being emitted from an object with a non-constant temperature. If you have a stove for example, you can calculate the total amount of joules being emitted every second (Watt, symbol P here) using this earlier mentioned formula: P = σ ⋅ A ⋅ T4 if you know the temperature and area (T and A, σ is a constant). Then you just multiply with during how many seconds and you have the total emitted joules during a certain time. But what if the temperature of the object that are emitting heat are not constant? The more joules emitted, the lower temperature, right? How can I calculate the total amount of joules being emitted during a certain time now?

Thank you

15. Jul 26, 2015

### Staff: Mentor

Then you need to know how the temperature changes with time, so you can do an integral:

$$E = \int \sigma A \left[ T(t) \right]^4 dt$$

If $T$ is constant, then this just reduces to multiplying the power by the length of time the object radiates.

16. Jul 26, 2015

### Qwertywerty

I still cannot understand why it would simply not be m*c*ΔT .

17. Jul 26, 2015

### Staff: Mentor

"Vacuum" means "no objects present", so a single object radiating into a vacuum means it's radiating into empty space with no other objects present.

18. Jul 26, 2015

### Staff: Mentor

See post #14; the OP wasn't actually asking the question you are answering here.

19. Jul 26, 2015

### Staff: Mentor

If there is no other energy source present, yes. But as your example of the stove shows, an object can emit heat while remaining at a constant temperature, if there is an energy source present (the stove is burning fuel to produce heat).

20. Jul 26, 2015

### Qwertywerty

No , my question was this - in any case , why would heat emitted by the body not be m*c*ΔT ?