Emphasizing Parameter Perspective
Consider a heated expanding system, i.e. heated expanding closed piston-cylinder. Next consider dQin as the heat in that drives expansion, dEsys as the change to the expanding system's energy and (PdV)atm as the lost work (AKA irreversible work) the following relation holds:
dQin = dEsys +(PdV)atm = dEsys + PatmdVsys (A)
Equation (A) is correct while it would be incorrect to write the following:
dQin = dEsys + (NkT)In(Vf/Vi) (B)
The only way that eqn (B) could be contemplated as being correct is if dEsys represented all the system's eneregy change except that associated with pressure and/or volume change! Even then it would still be lacking defining any work that was done! If you now wanted to include the work done then you would have to write:
dQin = dEsys + [(NkT)In(Vf/Vi)]sys + PatmdVsys (C)
Of course if dEsys remains the change to the expanding system's energy i.e. change to the summation of all its microscopic energies changes, then the correct way to write the equation remains (A)!!!
As stated in the internal energy blog: 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
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 “invisible microscopic energy”. 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 system’s kinematics i.e. the system’s energies associated with its molecular random motions, or if you prefer its kinetic energy. Based upon kinetic theory; a gaseous system’s pressure is a result of the various molecule’s 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 system’s molecular kinetic energies (translational plus rotational), then why would you add E to PV i.e. TS = E +PV or H=E+PV? It is completely illogical because the energy associated with the mechanical parameters pressure and volume of a gas is what is readily witnessed 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?
Again the only logical equation with clarity remains (A).
Note when I wrote my first edition of my book I have to admit that I was thinking in terms dE represently all the system's energy changes other than those associated with the mechanical parameters. It lead to illogical issues.