Rethinking Thermodynamics: Internal Energy & First law of thermodynamics
I trust that everyone had a merry xmas
Now for anyone interested I have rewritten my website on thermodynamics and added numerous blogs/discussions making it much more informative. See www.newthermodynamics.com.
I will be continually adding discussions/blogs to that site. If there is any blog that anyone feel that they or other members of this group want to discuss I will gladly it post it here. I will also try to post some of those blogs here over the future duration for two reasons. 1) hoping that there is interest here 2) an attempt to generate more interest in what I am saying. What I do not want to do is to take over this great website of your or anything like that , so I will trying to limit myself to blogging to you good folks perhaps once every few weeks sort of thing. And hopefully I will find the time to learn you editor for equations. for now I am using the rudimentary ways.
Internal Energy: How silly of us|
by Kent W. Mayhew
Consider the enthalpy (H) relation:
where E is the internal energy of the system, while P and V are pressure and volume respectively
As was previously discussed in the blog on entropy we could equally rewrite eqn 1) as
In thermodynamics the internal energy (E) is often taken to be the kinetic energy plus potential energy within a system. It sounds so simple. Who would challenge that.
What is the kinetic energy? It is the energy associated with the microscopic random disordered motions of the atoms and/or molecules within a system. This traditional perspective is sometimes referred to as the “invisible microscopic energy”.
See: (http://www.chem.libretexts.org/core/physical_and_theroretical_chemistry /thermodynamics/state_function/internal_energy
Again it sounds so logical until you realize that the pressure in a given volume of a gaseous system is defined by the system’s kinematics i.e. the system’s energies associated with molecular random motions. If you fail to appreciate this; then consider kinetic theory, wherein a gaseous system’s pressure is obviously a result of the various molecule’s kinetic energies. (see my blog concerning kinetic theory)
If the internal energy and pressure in a given volume are both a result of a gaseous system’s molecular kinetic energies, then why would you add E to PV as is done eqn 1) and/or eqn 2). It is completely illogical because the energy associated with the mechanical parameters pressure and volume of a gas is readily witnessed on a macroscopic scale.
How about a liquid? Well one website shows a glass of water and again wrongly insists that the internal energy is a result systems molecular random motion. (see: www.http://hyperphysics.phy.astr.gsu.edu/hbase/thermo/inteng.html).
What they also fail to state that we must also consider the water’s cohesive forces. Obviously for liquids the resulting pressure in a given volume is actually dominated by such cohesive forces. The cohesive forces within liquids (and solids) dominate over the kinetic energies of the molecules, therefore we do not witness changes to pressure within a given volume for liquids and solids in the same way that we do for gases.
Even so to try and say that it is the internal energy that changes is cumbersome if not wrong! Our reality for solids and liquids is that it is temperature at a given heat capacity that now defines the thermal energy within solids and liquids, and has little to do with volume at a given pressure. So why even use eqn 1) or 2) for liquids and/or solids?
Okay we learned in physical chemistry that enthalpy helps with our understanding of chemical reactions. And to an extent I will agree. However in chemical reactions when there is an isobaric volume change then we lost work, as we do in any process. And it is because of the energy associated with lost work in reactions that experience volume increases that a version of enthalpy is necessary.
But the above does not mean that enthalpy should be used when considering the energy changes within a system. Heck even a gaseous system has perverse logic when one does so. But for this blog let us just say it makes no sense when dealing with liquid’s or solids.
Now the above is going to scare those indoctrinated with traditional ways of dealing with chemical reactions. All I can say is do not blame the messenger! And yes I am sorry but your mature science is in dire need of an overhaul if you ever want to simplify it i.e. end its existence as a complication of the simple.
If you are still not convinced then let us look at this a slightly different way. Seemingly the energy of a system is traditionally defined in terms of the microscopic plus macroscopic energy, which all sounds great until you ask the following questions:
1) Should the macroscropic energy of a system not simply be a result of the summation of the system’s microscopic energies?
2) What about the energies that are not directly related to a system’s mechanical energy?
It remains a sad fact that traditional thermodynamics has become a complication of the simple in part because scientists have failed to ask the above two fundamental questions.
Our simple reality is that the summation of a system’s microscopic energies is what we witness as a system’s macroscopic energy! This is readily witnessed in gases but may not be so obvious when dealing with liquids or solids where intermolecular cohesive forces dominate. Therefore all of the mechanical aspects of a given system at a given temperature, is fully contained in the mechanical parameters, that being the system’s pressure (P) and volume (V) combined with cohesive forces!
THEREFORE a system’s internal energy should be taken to include all forms of energy that are not specifically mechanical (PV) related. Examples of such forms of energy being:
1) The bonding energy (U) between molecules;
2) The energy associated with a tensile layer;
3) The energy associated with matter; and
4) The potential energy associated with elevation.
It should be noted that the two mechanical forms of energy of a gas are its rotational and translational energies, as these can pass energy in manner that can do work. What about the vibrational. It is this author’s belief that although the vibrational energies can be exchanged between walls and gaseous molecules that the net result of this exchange will generally be a zero net energy exchange. In other words gaseous molecules give as much vibrational energy onto wall’s molecules as they receive, in which case vibrational energy belongs on the list. I.e.
5) Vibrational energy
6) Energy associated with inefficiencies
The above fits with the conceptualization that gaseous molecule’s vibrational energy is obtain from interactions with the surrounding blackbody/thermal) radiation. Also note one could argue that 5) belongs in 6).
Accordingly any illusion that a system’s macroscopic properties are not due to its microscopic properties is removed in our new perspective. Variations between the traditional and our new approach will become apparent throughout the ensuing sections of this text. Problems with traditional thermodynamics extend far beyond any misunderstanding of internal energy. That said the traditional poor consideration of internal energy does demonstrate how a science can become complication of the simple.
It should be stated that this all has to do with the fact that we all failed to realize the true virtues of lost work (remember lost work is the energy lost by expanding systems in upwardly displacing our atmosphere’s mass: W=PdV) , which then allowed the science to limit work to the isobaric isothermal case of:
And this then led to one blunder after another. How silly of us humans
Writing of the First Law
Consider that we are extracting energy out of a system. The first law of thermodynamics is traditionally written in terms extracted energy [Q(out)], internal energy change (dE) and work done (W):
Q(out) = dE(internal) – W 4)
To many the above makes sense, however if you realize that our conceptualization of internal energy was poor: See our blog wherein we discuss that our conceptualization of internal energy was perverse. See internal energy blog
An improve way of writing the first law would be in terms of a system total energy change (dEtot) rather than internal energy that being:
Q(out) = dE(tot) – W 5)
Sure eqn 4) and 5) are similar, but eqn 5) gives clarity in that it states the total (whole) system’s energy changes.
Now consider that energy is being put into a system, then in terms of thermal energy into a system (Ein), the first law is written:
Q(in) = dE(tot) – W 6)
In writing the first law W is the total work done by the system. If work is limited to the displacement of our atmosphere () then we would rewrite eqn 5) and eqn 6) respectively as:
Q(out) = dE(tot) – Watm = dE(tot) – PatmdV 7)
Q(in) = dE(tot) – Watm = dE(tot) – PatmdV 8)
Basically all the first law states is that “energy is conserved”.
In some ways we have done nothing but cut hairs as often the total energy change of a system may arguably be equal to the change of the system’s internal energy but this may depend upon one’s definition of internal energy. So why not keep things simple and write the first law in terms of the system’s total energy change. It avoids confusion and it tells us that the work done is done to system’s surroundings and/or devices attached to the system’s exterior.
One needs to realize that a gaseous system’s thermal energy and work are never equal, as we previously discussed. Remember our new perspective has limited the concept of internal energy change to energy changes other than those associated with work in PV space, i.e. internal energy change represents changes to energies that differentiate a system from being ideal, plus energies associated with things like tensile layers, plus possibly vibrational energy.
Interestingly writing the first law in terms of total energy change, as we do above, does remove the discussed issues. This means that the inefficiencies including the fact that not all of an ideal monatomic gaseous system’s energy increase can be used for work, as well as the energy associated with vibrational energies of polyatomic gases.
Although one could argue that the traditional interpretation of internal energy makes sense when applied to a liquid, it certainly does not when considering a gas wherein the macroscopic properties of the gas that being its volume at a given pressure is a direct result of the microscopic properties of that gas.
Since the consideration of internal energy is traditionally applied to all gas, luids and solids, then clearly our writing of traditional thermodynamics is in dire need of a rethink.