Efficiency

No manmade mechanical device or process is 100% efficient. Consider an engine that requires an energy input (Qin, or dQin), to power a bus that being Wbus. Since the engine is not 100% efficient, the energy input is always greater than the work out, i.e.:

          dQin > or = Wbus        (1)

In its simplest context: The engine’s efficiency (@) is simply the work out divided by the energy input:

         @=Wbus/dQin      (2)

Eqn (2) lacks specifics. How we now advance eqn (2) depends upon we specify systems. Reconsider the first law. In terms of heat into the system (dQin) and changes to a system’s internal energy (dEsys) plus any work done by that system (W) gives:

                       dQin = dEsys + W     (3)

   And if the only work that is the work done onto the surrounding atmosphere (Watm) by an expanding system i.e. lost work = PdV, then eqn (3) becomes:

dQin = dEsys + Watm = dEsys + (PdV)atm =  dEsys + PatmdVsys    (4)

   In the case of the bus’s movement, work is provided by an engine which does work onto the surrounding atmosphere plus work done in moving the bus (Wbus) :

                       dQin = dEsys + (PdV)atm + Wbus     (5)

    Now dEsys is a function the engine’s temperature increase i.e. dEsys= (Cv)enginedT,  while (PdV)atm is the work done onto the surrounding atmosphere and Wbus is the work done in moving the bus. However we must also consider friction between the bus and  its surroundings i.e. drag between moving bus & atmosphere, as well as friction between the bus’s wheels and the road, plus any friction internal to the bus   

 Obviously, this can be made as complicated as we need to. Perhaps we care to analyze the bus’s movement in terms of the gasoline, air mixtures, i.e. internal engine combustion. The combustion process involves expansion hence increases the atmosphere’s energy (W=PdV=PatmdV). And all of the energy of combustion cannot be extracted to do work, as discussed in the work vs energy blog.   

Interestingly in traditional thermodynamics all of the above inefficiencies were (wrongly?) blamed upon the second law. Inefficiencies can be complicated enough. Do we really have to explain such things terms of phase space, entropy and the second law?

Of course to this author all that was wrongly explained by the second law can be explained in simpler terms. It is like making scrambled eggs. You can say put the fork in a hand and then wisk eggs & milk vigorously and then cook in fry pan. Or you can put elemental parts of various components of the yolk into its own infinitesimal volumes and get into the vortices of each volume. If the object is to eat breakfast then the wisking and cooking explanation will do just fine.  

Understandably, no cyclic engine that has friction in any form and/or displaces our atmosphere can never ever be 100% efficient hence power the elusive perpetual motion machine. For those of you not familiar with the concept: A perpetual motion machine is a machine that keeps on going and going, without the need of the addition of energy from an external source, into one (or more) of its cycles. As we are about to find out there is more to understanding efficiency than this i.e. the above described efficiencies are idealistic, let us now investigate the reality.