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 wrongly thought to be the system's 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 either:

1) the kinetic energy plus potential energy within a system.

2) The summation of the system's microscopic energies

Let us consider 1): What is the system's 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 its molecular random motions, or if you prefer its kinetic energy. 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 traditional kinetic theory or our new improved kinetic theory, which clearly 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.

One can readily envision that the above 2) summation of the system's microscopic energy is nothing short of a fancy way of saying the system's total energy, which is a simple way of sayings its kinetic plus potential energy. Again this imposes the question of if P and V are a result of these energies then why add PV to E? 

What about about a liquid as a system? 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, i.e. 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 manner 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.  Of course this clarity is only obtained by rewritting eqn 3) as:


       (TdS)sys = dEsys + (PdV)atm =  dEsys + PatmdVsys        4)


Where subscripts "sys" and "atm" respectively signifies the expanding system and atmosphere.


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


Next consider the implications to Enthalpy: H= E +PV




   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 (E)  is the energy 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."
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