Probably many, most or all of my readers wonder why I continue with this theme when it’s so completely obvious..
Well, most people haven’t studied thermodynamics and so an erroneous idea can easily be accepted as true.
All I want to present here is the simple proof that thermodynamics textbooks don’t teach the false ideas circulating the internet about the second law of thermodynamics.
So for those prepared to think and question – it should be reasonably easy, even if discomforting, to realize that an idea they have accepted is just not true. For those committed to their cause, well, even if Clausius were to rise from the dead and explain it..
On another blog someone said:
Provide your reference that he said heat can spontaneously flow from cold to hot. And not from a climate ‘science’ text.
I had cited the diagram from Fundamentals of Heat and Mass Transfer by Incropera and DeWitt (2007). It’s not a climate science book as the title indicates.
However, despite my pressing (you can read the long painful exchange that follows) I didn’t find out what the blog owner actually thought that the writers of this book were saying. Perhaps the blog owner never grasped the key element of the difference between the real law and the imaginary one.
So I should explain again the difference between the real and imaginary second law of thermodynamics once again. I’m relying on the various proponents of the imaginary law because I can’t find it in any textbooks. Feel free to correct me if you understand this law in detail.
The Real Second Law of Thermodynamics
1a. Net heat flows from the hotter to the colder
1b. Entropy of a closed system can never reduce
1c. In a radiative exchange, both hotter and colder bodies emit radiation
1d. In a radiative exchange, the colder body absorbs the energy from the hotter body
1e. In a radiative exchange, the hotter body absorbs the energy from the colder body
1f. This energy from the colder body increases the temperature compared with the case where the energy was not absorbed
1g. Due to the higher energy radiated from a hotter body, the consequence is that net heat flows from the hotter to the colder (see note 1)
The Imaginary Second Law of Thermodynamics
2a. – as 1a
2b. - as 1b
2c. - as 1c
2d. - as 1d
2e. In a radiative exchange, the hotter body does not absorb the energy from the colder body as this would be a violation of the second law of thermodynamics
Hopefully everyone can clearly see the difference between the two “points of view”. Everyone agrees that net heat flows from hotter to colder. There is no dispute about that.
What the Equations Look Like for Both Cases
Now, let’s take a look at the radiative exchange that would take place under the two cases and compare them with a textbook. Even if you find maths a little difficult to follow, the concept will be as simple as “two oranges minus one orange” vs “two oranges” so stay with me..
Here is the example we will consider:
We will keep it very simple for those not so familiar with maths. In typical examples, we have to consider the view factor – this is a result of geometry – the ratio of energy radiated from body 1 that reaches body 2, and the reverse. In our example, we can ignore that by considering two very long plates close together.
E1 is the energy radiated from body 1 (per unit area) and we consider the case when all of it reaches body 2, E2 is the energy radiated from body 2 (per unit area) and we consider that all of it reaches body 1.
We define Enet1 as the change in energy experienced by body 1 (per unit area). And Enet2 as the change in energy experienced by body 2 (per unit area).
Radiation Exchange under The Real Second Law
E1 = εσT14; E2= εσT24 (Stefan-Boltzmann law)
Enet1 = E2 – E1 = εσT24 – εσT14
Enet2 = E1 – E2 = εσT14 – εσT24
Therefore, Enet1 = -Enet2
Under The Imaginary Second Law
Enet1 = – E1 = -εσT14
Enet2 = E1 – E2 = εσT144 – εσT24
Therefore, Enet1 ≠-Enet2 ; note that ≠ means “not equal to”
This should be uncontroversial. All I have done is written down mathematically what the two sides are saying. If we took into account view factors and areas then the formulae would like slightly more cluttered with terms like A1F12.
In the case of the real second law, the net energy absorbed by body 2 is the net energy lost by body 1.
In the case of the imaginary second law, there is some energy floating around. No advocates have so far explained what happens to it. Probably it floats off into space where it can eventually be absorbed by a colder body.
Alert readers will be able to see the tiny problem with this scenario..
What the Textbooks Say
First of all, what they don’t say is:
When energy is transferred by radiation from a colder body to a hotter body, it is important to understand that this incident radiation cannot be absorbed – otherwise it would be a clear violation of the second law of thermodynamics
I could leave it there really. Why don’t the books say this?
Engineering Calculations in Radiative Heat Transfer, by Gray and Müller (1974)
Note that if the imaginary second law advocates were correct, then the text would have to restrict the conditions under which equation 2.1 and 2.2 were correct – i.e., that they were only correct for the energy gain for the colder body and NOT correct for the energy loss of the hotter body.
Heat and Mass Transfer, by Eckert and Drake (1959)
Note the highlighted area.
Basic Heat Transfer, M. Necati Özisik (1977)
Note the circled equations – matching the equations for the “real second law” and not matching the equations for the “imaginary second law”. Note the highlighted area.
Heat Transfer, by Max Jakob (1957)
Note the highlighted section, same comment as for the first book.
Principles of Heat Transfer, Kreith (1965)
Note the highlighted sections. The second highlight once again confirms the equation shown at the start, that under “the real second law” conditions, Enet1 = – Enet2. Under the “imaginary second law” conditions this equation doesn’t hold.
Fundamentals of Heat and Mass Transfer, Incropera and DeWitt (2007)
Note the circled section. This is false, according to the advocates of the imaginary second law of thermodynamics.
And the very familiar diagram shown many times before:
There are some obvious explanations:
1. Professors in the field of heat transfer write rubbish that is easily refuted by checking the second law – heat cannot flow from a colder to a hotter body.
2. Climate science advocates have crept into libraries around the world, and undiscovered until now, have doctored all of the heat transfer text books.
3. (My personal favorite) Science of Doom is refuted because these writers all agree that net heat flows from the hotter to the colder.
4. Look, a raven.
Relevant articles - The Real Second Law of Thermodynamics
Note 1 – Strictly speaking a hotter body might radiate less than a colder body – in the case where the emissivity of the hotter body was much lower than the emissivity of the colder body. But under those conditions, the hotter body would also absorb much less of the irradiation from the colder body (because absorptivity = emissivity). And so net heat flow would still be from the hotter to the colder.
To keep explanations to a minimum in the body of the article in 1e and 1f I also didn’t state that the proportion of energy absorbed by each would depend on the absorptivity of each body.