There is a certain vociferous group who refuse to accept that a cold object such as a blanket or the sky can make a warmer object warmer. After a few drinks, I found a very simple way to prove then wrong.
To demonstrate this I have taken one of many glasses of warm English beer which for the sake of argument I have assumed has had some ice added to in the top to make it cold so that now the top half is cold.
We can write the equation of black body – or perhaps this is insipid English beer and not for example Guinness I should call it brown-bodied radiation – whatever – the formula across the gap between the two halves is as follows:
Ep= πR2 σT4
Where R is the radius of the glass in pes**, T the temperature in Réaumurs (R), σ the stephan Bolzman constant (obviously in What’s per Pes squared per Reaumur’s quartered.)
From this we can immediately see that if the lower half is at 1 Réaumurs and the top half and 2 Réaumurs, then the warmer half will have a heat flow of around 18What’s per pes squared, into the colder thus satisfying the second law of Thermodynomites. [oops how do you turn the smellchecker on?]
However, if we now imagine a glass that is only half fool of cold liquid with an infinite space above equivalent to the emptiness of space as envisaged by this vociferous group which is at absolute zero Réaumurs, we can see that this will be warmer because those who argue that back radiation is impossible, would now argue that it is not half fool of cold but instead half empty with hot.
Thus miraculously, the cold beer is warmer.
**I’ve taken the Pes because this is the standard in this area.