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 = AεσT^{4} [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.