A New Thermodynamics

By Kent W. Mayhew

Internal Energy: What is It


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 the mechanical parameters pressure and volume respectively 


As was previously discussed in the blog on entropy we could rewrite eqn 1) in terms of entropy and temperature 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 or if you prefer its kinetic energy. For example based upon kinetic theory; a gaseous systemís pressure is a result of the various moleculeís kinetic energies (translational plus rotational). This statement remains true whether you consider traditionalkinetic theory or my new improved kinetic theory that better explains empirical findings.

  If the internal energy and pressure in a given volume are both a result of the same gaseous systemís molecular kinetic energies (translational plus rotational), 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 what we readily witness 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 realize is 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.

How do we resolve this:

   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 not only explain why useful processes are irreversible but it also add sense to the science by limiting work to the isobaric isothermal case of change to eqn 2). That being::


       TdS=dE+PdV   3)


  In 3) isothermal entropy change (TdS) is equated to the change in the system internal energy (dE) plus the work done externally to the system that being the irrevdersible work done onto the surrounding atmosphere as defined by: PdV.


For further understanding see blogs onisobaric vs isometric heating and/or Specific heats and/or latent heat. What about the implications to the first law? click here to see First Law Blog.


Enthalpy Issues

Reconsider physical chemistry where enthalpy (H=E+PV) helps with our understanding of reactions. Again enthalpy change is limited to isothermal chemical reactions that involve isobaric volume change i.e.Lost Work. And it is because of the energy associated with lost work in reactions that experience volume increases that this version of enthalpy change remains necessary:

   dH=dE+PdV    4)

 However the enthalpy change should not be used when considering the energy changes within a system because PdV is external (surroundings) while dE is internal to the system.

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 our reality.

Moreover, 4) means that we should not think in terms of isometric pressure change (VdP), as we often do in the differential shuffle. The reason is in part because PdV in eqn 4) is irreversible work done onto the surrounding atmosphere. In other words the atmosphere cannot do work onto a system that has just experienced isobaric isothermal expansion.

Think about it. If we then compress the above considered system, then it is not the atmosphere returning energy, rather it is whatever mechanism that is being used to compress the system that does the work in compression.

Certainly compression of a gaseous system will increase both a systemís ability [d(PV)] and its potential (VdP) to do work. However it also increases that gaseous  systemís energy but only if the compression results in a gaseous temperature increase which means the systemís total energy (AKA internal energy) has increases as it would as a function of its temperature.

If the above compressed systemís temperature remains constant, then only its potential to do work increases. Note in order for a compressed system to remain isothermal then it should be compressed quasi-statically so that any created heat can exit through the systemís walls as radiated heat.

The internal energy may be better viewed this way

Perhaps a systemís internal energy should be taken to include all forms of thermal energy that are not specifically mechanical (PV) related. Examples of such forms of energy being:

1)   The thermal energy associated with matter's kinetic energy (translational plus rotational).

 2)  The thermal energy associated with matters intermolecular vibrations.

 3)  The thermal energy associated with matters intramolecular vibrations.


   All of the above can be considered to be direct functions of measurable temperature.


   Do we add to the above list  for internal energy potential energies such as:

        4)  The bonding energy (U) between molecules.

         5)  The potential energy associated with elevation.


    How about the energy associated with tensile layer?

         6)  Energy energy associated with any tensile layer.


    Certainly such potential energy are not witnessed when measuring a systemís energy with a thermometer. However when potential transforms into kinetic then it has a temperature functionality. 


 Ditto for when a tensile layers forms it requires thermal energy, which generally must be absorbed from the surrounding liquid's thermal energy. Conversely  and when it collapses it releases energy, which is generally thermal if its collapse is relatively slow. Interestingly if a tensile layer collapses rapidly, as is often witnessed in sonoluminescence, then the energy released can resemble the blackbody radiation attributed to high temperature bodies i.e. 3000 degrees kelvin. 




   Note there are those who believe that the energy associated with tensile layers is due to free energies which are traditionally calculated using the dreaded differential shuffle. Trust me when I say that there are other explanations, and I may present some in the not to distant future. Future book?


 It should be noted that the two mechanical forms of energy of a gas are its rotational and

translational energies, as these can do work onto their surroundings. And they are responsible for what we measure as the systemís mechanical parameters volume (V) and pressure (P). This 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.




As discussed in numerous other blogs throughout this webs. The internal energy (dE) is the energy change of the system that being a summation of all the system's microscopic energies that are a function of system's temperature. It is most readily calculated by  multiplying the systemís temperature change by its heat capacity (CvdT).  Work done by a system is external to that system and is defined in terms of the surrounding's mechanical parameters is surroundings our atmosphere then the irreversible lost work is  Wlost=PdV.


 If work is done onto a system then it can be witnessed as either a temperature increase into that system and/or a pressure increase. A pressure increase without a temperature does not necessarily mean the systemís energy has change, rather can be viewed as an increase in that systemís potential to do work.



Copyright Kent W. Mayhew

Internal Energy: What is it
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Sommerfield quote:"Thermodynamics is a funny subject. The first time you go through it, you don't understand it at all. The second time you go through it, you think you understand it, except for one or two small points. The third time you go through it, you know you don't understand it, but by that time you are so used to it, so it doesn't bother you any more."
This website is copyright of Kent W. Mayhew who in 2018 resides in Ottawa Ontario Canada
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