A New Thermodynamics

By Kent W. Mayhew

Implications to First Law


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



   Writing of the First Law 

Consider that we are extracting energy out of a system. The first law of thermodynamics is traditionally written,1,2 in terms extracted energy (Qout), internal energy change (dE) and work done (W):

      Qout = dE(internal) – W                eqn 1)

   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:

     Qout = dE(tot) – W                      eqn 2)

Sure eqn 1) and 2) are similar, but eqn 2) gives clarity in that it states the total (whole) system’s energy changes.

 Moreover the understanding behind eqn 2) is that work is done through the system walls onto something outside of the system, such as the surrounding atmosphere (Watm=PatmdV)! This is not the case for traditionally accepted eqn 1) wherein the implication (although not clearly stated) is that the work is done to the system's walls, irrelevant of whether the walls are real or imaginary. 

   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:

     Qin = dE(tot) – W                     eqn 3)

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 2) and eqn 3) respectively as:

      Qout = dE(tot) – Watm =  dE(tot) – PatmdV            eqn4)


       Qin = dE(tot) – Watm =  dE(tot) – PatmdV            eqn4)


Basically all the first law states is that “energy is conserved”. And in that sense nothing has changed. 


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 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.

Hence tradiationalist may argue that I am talking semantics. I am not, I am really talking clarity vs ambiguity!

One needs to realize that a gaseous system’s thermal energy and work are never equal, as we discussed throughout this section. 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 differentiates 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.


Copyright Kent W. Mayhew



1.  “Fundamentals of Statistical and Thermal Physics”, F. Reif, McGraw-Hill, New York, 1965

2.  “Statistical Physics”, F. Reif, McGraw-Hill, New York, 1967


First Law: Implications to
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