Carnot Engine/Cycle

In 1824, Sadi Carnot envisioned the classic idealistic theoretical heat engine, which is traditionally used to educate young aspiring scientists, known as Carnot Engine/Cycle. Conceptually, his cycle was envisioned as a methodology for extracting energy/work from a constant temperature heat reservoir to be used in some cooler temperature surrounding, or, system. The cycle illustrated in Fig 9.12 to the right, which is based upon traditional interpretations for the compression/expansion cycle of an ideal gas operating between two constant temperature regions, wherein all steps in the process are deemed reversible. Note I discuss the cycle in more detail in my book. However the discussion below is perhaps an improvement over what is said in the book.

The concept of all steps being reversible means that the Carnot cycle is an idealized heat engine that is often traditionally taught in thermodynamics. This author sees little value in it and will briefly discuss why.

The Carnot cycle wrongly considers that energy is never lost, hence it is a thermodynamic dream perpetual motion engine. Most thermodynamic engines attain their power from an expanding gas in one or more steps of their cycle. Consider any engine wherein heat dQ is required for an isobaric expansion process, e.g. the isobaric expansion of a piston-cylinder apparatus filled with an ideal gas. The issue becomes how can this be done at 100% efficiency? It would need to expand due to a heat source and more importantly any realistic system would have to displace our atmosphere, resulting in lost work (W=PdV)!  For blog on expanding piston-cylinder

  One cannot avoid this fact: Irreversible lost work is going to occur when any gas experiences  isobaric expansion (PdV) and is surrounded by an atmosphere. Hence any concept of thermodynamic perpetual motion engine/machine here in Earth dies right here. And of course other frictional based factors come into play.

 From the temperature side, collecting and channeling thermal energy is not always a simple task. Specifically thermal energy/heat tends to disperse radially, unless properly contained/constrained.   

 A good on-line examples demonstrating the traditionally accepted analysis for the Carnot cycle is:

A)http://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Thermodynamics/Thermodynamic_Cycles/Carnot_Cyclehttp://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Thermodynamics/Thermodynamic_Cycles/Carnot_Cycle

    Why the Carnot cycle is illogical: Start by looking at Fig 9.12 to the right

Step 1). “Reversible isothermal expansion”; From points 1 to 2: Put the engine in contact with the hotter heat reservoir at T1, and then allow it to isothermally expand from: V1 to V2.  If it were not in contact with the hot reservoir, then the gas’s temperature would have to decrease as it expands, i.e. as it does work. The gas’s temperature remaining constant requires energy. Accordingly, isothermal expansion requires heat in [Qin  ].

Analysis

In order to remain isothermal:  Qin = PatmdV = work done onto atmosphere = lost work

Since the above is lost work the process cannot be reversible

   Step 2). “Isentropic expansion” as an adiabatic process; From points 2 to 3: The hot engine is thermally re-isolated and its volume is allowed to expand from V2 to V3, until its temperature decreases back to T. Herein the engine cools as it does work in displacing its surroundings i.e. atmosphere.

     Analysis

     Again expansion means that work is done onto the atmosphere as defined by Watm = PatmdV. And since no energy enters then the gas’s temperature must decrease. However the expansion is neither an isothermal or isobaric process. However for an ideal gas if its pressure decreases while its volume increases then that gas’s energy only changes due to its temperature change, which in this case is only due to work done onto the atmosphere  

   Step 3). “Reversible isothermal compression”; From points 3 to 4: The engine is now put into thermal contact with a cooler heat reservoir at T ' and the gas is now compressed: V3 to V4. In traditional conceptualization the gas gives up energy [Qout], i.e. the system’s total energy has decreased.

 Analysis

 Putting a gas into thermal contact with a cooler system would normally mean that the gas’s thermal energy decreases. If considering a monatomic ideal gas then its energy decreases by: 3NkdT/2.  Can we now can say Qout=3NkdT/2? Okay the gas cooled in Step 2), so we can argue that 3NkdT/2 is the energy change in Step 2).   

Moreover, the above would be the case if compression does not result in a temperature increase of a gas! Specifically: Since intermolecular collisions are inelastic then there is a pressure-temperature relationship that cannot be when compressing a rigid closed insulated systems. Okay this system is not closed insulated, nor rigid, but this does not mean that it does not experience a temperature increase as its pressure increases.

 One can see that Step 3) is illogical on many levels   

Step 4). “Isentropic compression” as an adiabatic process; From points 4 to 1: The engine/cycle starts at a colder temperature T 'and is thermally isolated (100% insulated). The gas is slowly compressed hence its volume decreases from; V4 to V1 and its pressure increases; P4 to P1, which causes to the gas’s temperature increasing to back to T1.  And thus completes the illogical cycle.

Analysis

 The insinuation is that the work lost (lost work) in Steps 1) and Step 2) can simply be regained. This is completely illogical because the atmosphere can never do work onto an isobaric system! The work done in Step 1) and Step 2) was lost work hence never to be reversed.

The other illogical contemplations in the traditional understanding of the Carnot are just illogical consequences of not understanding lost work and not realizing that intermolecular collisions are NOT elastic.