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I write this article as a placeholder to send people to – and as a request for information.

On another blog, there was a confused article posted about the earth’s energy balance. Within the article was this statement:

Earth is a grey body, because it has volume, a black body does not have volume, simply that is the end of “the controversy”.

As I said in my comment to the article:

I have seen similar inaccurate comments before but can’t fathom where they came from.

A followup comment to mine reinforced the point that I just don’t understand:

  • what many people believe about blackbodies, or
  • what many people believe conventional climate science believes about blackbodies (and why it’s supposed to be wrong)

So this is a request for clarification of “the problem”

I will post examples of changing temperature for a blackbody and a non-blackbody. But because of my lack of understanding of “the problem” I have no idea if these examples will highlight particular areas of disagreement, or are completely accepted by all.

Just before the examples:

My understanding, gained from dull textbooks on the subject of heat transfer and atmospheric physics:

The difference between a “grey body” and a “black body” is this:

1. A blackbody has an emissivity of 1. So energy radiated in W/m², E = εσT^4, where ε=1.
2. A non-blackbody has an emissivity >0 and <1. So energy radiated in W/m², E = εσT^4, where ε<1.

No other physical properties are related to this parameter called emissivity, or to the difference between “blackbodies” and “non-blackbodies“.

Unrelated parameters:

  • Mass
  • Specific heat capacity
  • Color
  • Thermal conductivity
  • Viscosity
  • Density

I could go on, but I’m sure the point is made.

So, onto the two examples.

Example 1 – A Blackbody

Let’s consider a body of mass, m = 1kg with specific heat capacity, cp = 1000 J/kg.K.
Therefore, heat capacity, C = 1000 J/K.
Surface area, A = 2 m².
Emissivity, ε = 1 (a blackbody).

Temperature (at time, t=0) = 300K
Background temperature = 0K (lost in the vastness of space, see note 1)

No external energy is supplied after time, t=0. The body is suddenly placed in the vastness of space. What happens to temperature over time?

The body radiates:

E = AεσT4 [1] Note, really we should write E(t) and T(t) to show that E and T are functions of time

Change in temperature with time:

dT/dt = E/C [2]

Here is the change in temperature with time:

Example 2 – A non-blackbody

Exactly the same as Example 1 – but ε = 0.6 (not a blackbody).

Here is a non-blackbody result:

You can see the form of the result is similar but the temperature drops more slowly – because it is emitting radiation more slowly.

Conclusion

The equations are the same for both examples. The other physical parameters are the same for both. The results are similar. There is nothing startlingly different about a solution with a blackbody and a body with an emissivity less than 1.

Well, that’s my take on it.

Blackbodies appear to be believed to have characteristics unknown in textbooks. I hope some people can explain their “issue” with blackbodies. Or what “the problem” really is.

Notes

Note 1: Yes, the background temperature of space is 2.7K, but using 0K just makes the maths easier for people to follow.

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