Problems with Dr. Roy Spencer’s picture in his “Yes Virginia” paper
In order to explain a physical process the mathematics that has been developed to describe it must be a good representation of all of the steps. What Dr. Spencer has done with his article, ‘Yes, Virginia, Cooler Objects Can Make Warmer Objects Even Warmer Still‘ is to take the basic Stefan Boltzmann equation (SBe) that I described in my previous article and neglected to consider the changes required in the adjustable parameters, with the exception of T1, by his addition of the second plate.
Dr. Pierre R Latour has already pointed out errors by Dr. Spencer in Latour’s ‘No, Virginia‘ rebuttal. The full email exchange between Spencer and Latour may be studied here.
Without a doubt the energy flux to the container from the heated plate will change. The A and ε are no longer the same as before the addition, and have to be included inside the bracketed part of the equation, with a corresponding time dependent variable as the emissivity and temperature now become a function of time. Note that T2 in the SBe is neglected in the picture presented to attempt to describe the effect.
Following on in his discussion Dr. Spencer boldly asserts that “back radiation” is occurring although nowhere in the illustration is any evidence as to how it is possible.
In our physical picture of the universe the available states of energy are described using the constant Max Planck invented as a last resort to describe black body radiation. His constant labeled “h” is the heart and soul of all quantum mechanics.
The theory states that all natural processes lead to the distribution of the available energy among all the states into which it can go in the universe according to the laws of probability. Rudolf Clausius labeled the concept entropy. It is described by a simple equation in which entropy is given the label S. The simple equation which describes all of the thermodynamics of the universe is written as: S = k (logP) . k is Boltzmann’s constant (which is part of the σ in the Stefan-Boltzmann equation.) P is the probability of finding the universe with the energy distributed the way it is at that moment in time.
The probability of finding all of the energy in the universe concentrated at an incredibly tiny spot like it was when it was created at the big bang is incredibly small and so the entropy is almost zero. The probability that the energy is distributed around among all of the ways in which is can now be found is infinitely larger and the thermodynamic way of describing this fact is to say that the entropy has got bigger.
We have no way of knowing what the entropy of the universe is at the present time. We do know that all of the energy states are not populated equally and all of the natural processes are trying to equalize the population of all of the states. That is why heat flows from hot bodies to cold ones and why the theoreticians worry about the heat death of the universe when everything is at the same temperature. At that point energy can no longer flow from place to place, the entropy is the largest it can be, and everything stops. (Does time stop as well?)
We can now consider a great simplification which is the basis of all thermodynamics and is used to describe the behavior of all of our systems in which energy is transferred. It forms the basis for the design of the jet engines that push the planes and the refrigeration systems that produce the ice in the hockey arenas and unfortunately there are still people that do not believe it is true.
All we have to worry about in any physical process where the transfer of energy is involved, and it makes no difference how we do it, whether it is by radiation, or a diesel engine in a car, is that the entropy has to increase during the process.
The change in entropy during a process in which energy is transferred is defined by another simple equation.
It is: dS = dH/T .
dS is the short hand for “the change in entropy” and dH is the shorthand for the amount of energy that is involved in the process and T is the absolute temperature at which the change is taking place. Heat (energy) when it is taken out of a system is defined as being negative and is written with a minus sign (-dH) and heat put into a system is defined as positive.
Now we have learned all of the necessary physical laws, and although they are profound, are easy to use in their application mode. The difficulty is that it is a concept and doesn’t have the impact that learning the law of gravity had on us when we first became acquainted with its effects.
Let us apply what we have learned in this short lesson to the transfer of energy from the cold plate to the hot one by moving some energy from one plate to the other. During the transfer process we can break down the change in entropy into two steps, one made at the beginning of the transfer process and the other at the end. The changes in the entropy are different in the two steps. There is a negative change where the energy is taken out and a positive change where the energy is put in.
Now let us look at what happens if we were to move a little bit of energy we shall call Q from one plate to another. To distinguish our two plates we will label the parts of our equations that we use with the subscripts “h” for hot and “c” for cold. So now the change in entropy at the two ends of the transfer process are labeled dSh for the change at the hot plate and dSc for the change at the cold plate. The exact expressions for the changes are:
dSh = Q/Th dSc = Q/Tc
Now we can see how the direction of the transfer would affect the total entropy change in the transfer of the energy. The amount of energy we move doesn’t change during the move but the amount of the change in entropy in the system depends on the temperature at which we move the bundle of energy. The change is bigger at the cold plate.
If we are moving energy from the hot plate to the cold plate we are taking it out of the hot plate and we keep track of the process in our mathematics by giving it a negative sign in our equation like we described above. The value of dSh is negative when we take the energy bundle out of the hot plate. When we put the bundle of energy into the cold plate according to our mathematical rules, dSc is positive. If we now sum the two bits to describe the total transfer process we get a positive value, the entropy has increased and the transition is permitted.
If we try to move a bundle of energy from the cold plate to the hot one we are taking energy out of the cold plate so the bit ot entropy involved in the action would be negative and the bit involved at the hot end of the transition would be positive. As the entropy bit at the cold end is larger than the bit at the hot end the sum of the two bits necessary to describe the total process would be negative, the transition would result in a decrease in the total entropy and so is forbidden and doesn’t take place.
We have learned a little thermodynamics and also a little quantum mechanics at the same time and didn’t even know it. And the beauty of it all is that we are reminded about what we have learned every time we write down the Stefan-Boltzmann equation in its more generalized form. But even better we no longer have to argue about the oxymoronic expression “backradiation”, and still better everyone now can use the revised NASA diagram called EARTH’S ENERGY BUDGET issued in 2011 which no longer displays backradiation as part of the energy flow to and from the earth.
Nothing in this description requires more than a look into a good first year university Physics text book. Unfortunately there are errors in many of the more popular ones in use today.
Trackback from your site.