A New Thermodynamics

By Kent W. Mayhew

Internal Energy: How silly of us


Kent W. Mayhew         (see how differential equations are poorly applied: Differential Shuffle)


     Consider the enthalpy (H) relation:


   H=E+PV        1)


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


 TS=H=E+PV     2)


 See blog: Entropy


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 ďinvisible microscopic energyĒ.

See: (click here) 

Again it sounds so logical until you realize that the pressure in a given volume of a gaseous system is defined by the systemís kinematics i.e. the systemís energies associated with molecular random motions. If you fail to appreciate this; then consider kinetic theory, wherein a gaseous systemís pressure is obviously a result of the various moleculeís 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 systemís 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: click here ) 

   What they also fail to state that we must also consider the waterís 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. (see my blog on Lost Work). 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 liquidís 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 systemís microscopic energies?

2)  What about the energies that are not directly related to a systemís 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 systemís microscopic energies is what we witness as a systemís 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 systemís pressure (P) and volume (V) combined with cohesive forces!   

THEREFORE a systemís 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 authorís 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 wallís molecules as they receive, in which case vibrational energy belongs on the list. I.e.


         5) Vibrational energies


 The above fits with the conceptualization that gaseous moleculeís vibrational energy is obtain from interactions with the surrounding blackbody/thermal) radiation.



  Any illusion that a systemís 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 (Please see blog on lost work) , which then allowed the science to limit work to the isobaric isothermal case of:


   W=TdS=dE+PdV   3)


And this then led to one blunder after another. How silly of us humans


What are the implications to the first law? click here to see First Law Blog




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, liquids and solids, then clearly our writing of traditional thermodynamics is in dire need of a rethink.  



Copyright Kent W. Mayhew

Internal Energy: How Silly of us
thermowebsite2030013.jpg thermowebsite2030010.jpg thermowebsite2030008.jpg thermowebsite2030005.jpg thermowebsite2030004.jpg thermowebsite2030003.jpg thermowebsite2030001.jpg
Help support this site