Carnot cycle system

Figure 28. The scheme and SPEED for Carnot cycle system ...

Figure 30. Mediator loop and thermodynamic compass for the whole Carnot cycle system.

Because the gas in the Carnot cycle starts and ends at the same state, the system s entropy does not change during a cycle. Now apply the second law to the universe for the case of the Carnot cycle. Because the processes are reversible, the entropy of the universe does not change by Equation 2b. This can be written ... 

The maximum theoretical work Wn, obtainable from a system was derived by Carnot who considered the transformation of heat energy into work when a perfect gas in a cylinder with a piston was taken through a reversible cycle (the Carnot cycle), in which the system was almost at equilibrium during each step of the cycle. It was shown that... 

We now take the system round a reversible Carnot cycle, the reversibility for such a system, in the limit, having been previously demonstrated. 

Figure 6.11. Sketch of the Q2-Q1 coordinate system for possible Carnot cycles.

In carrying out a (reversible) Carnot cycle, we can place a two-phase system instead of an ideal gas into a cylinder. A suitable two-phase system is... 

During process 4-1, heat is transferred isothermally from the working substance to the low-temperature reservoir at Tl. This process is accomplished reversibly by bringing the system in contact with the low-temperature reservoir whose temperature is equal to or infinitesimally lower than that of the working substance. The amount of heat transfer during the process is 641= f TdS = Ti Si — S4), which can be represented by the area 1-4-5-6-1 Q41 is the amount of heat removed from the Carnot cycle to a low-temperature thermal reservoir. 

Suppose an ideal regenerator is added to an Ericsson cycle. The regenerator would absorb heat from the system during part of the cycle and return exactly the same amount of heat to the system during another part of the cycle. What would be the difference between the Ericsson cycle efficiency and the Carnot cycle efficiency ... 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

The cell temperature T c is again the temperature T of the process environment. The work wtcc produced by the Carnot cycle CC increases with higher Tpc and the work in/ i crev produced by FC decreases with lower 7jc as already expected. The work wtSyst of the system is independent of 7 if (or nearly independent in the case of the simplified process). The FC operates reversibly in both cases but the Carnot cycle CC does not operate completely reversible in the simplified process caused by the fact that a small part of the waste heat of FC is needed to heat air and fuel. The practical benefit of this combined fuel cell-heat reference cycle is the opportunity for using exergetic efficiencies to describe the operation of real cycles with this very simple model. The needed exergetic efficiency f is defined as... 

The system efficiency jjsyst increases with the cell temperature TFC for all exergetic efficiencies fc < 1 until a maximum is reached. The maximum efficiency jjsyst moves to a higher temperatures for decreasing exergetic efficiencies fc The influence of the Carnot cycle dominates at lower temperatures Tpc and lower exergetic efficiencies fc-... 

In Section 3.3 we concluded that an isolated system can be returned to its original state only when all processes that take place within the system are reversible otherwise, in attempting a cyclic process, at least one work reservoir within the isolated system will have done work and some heat reservoir, also within the isolated system, will have absorbed a quantity of heat. We sought a monotonically varying function that describes these results. The reversible Carnot cycle was introduced to investigate the properties of reversible cycles, and the generality of the results has been shown in the preceding sections. We now introduce the entropy function. 

We continue with a reversible heat engine operating in a Carnot cycle, but center our attention on the working substance rather than on the entire system consisting of the heat engine, the work reservoir, and the two heat reservoirs. For such a cycle we can write... 

This chapter establishes a direct relation between lost work and the fluxes and driving forces of a process. The Carnot cycle is revisited to investigate how the Carnot efficiency is affected by the irreversibilities in the process. We show to what extent the constraints of finite size and finite time reduce the efficiency of the process, but we also show that these constraints still allow a most favorable operation mode, the thermodynamic optimum, where the entropy generation and thus the lost work are at a minimum. Attention is given to the equipartitioning principle, which seems to be a universal characteristic of optimal operation in both animate and inanimate dynamic systems. 

The Carnot cycle engine achieves what we are looking for, a conversion of heat into work, with return of the engine to its initial state. We note, however, that in order to complete the cycle, we have paid a price. In the isothermal compression at Tc, some of the work produced in the expansion has to be used up to compress the system, finding its way into heat at the cold reservoir temperature. 

An important measure of the quality of an engine is its efficiency, [the fraction of the energy that it removes from a high temperature reservoir (the heat term in step I) that it converts into work].7 For the Carnot cycle engine to work as efficiently as possible, the heat transfers should be reversible. Thus, the heat transferred to the system in step I should be from a heat reservoir at temperature Th, and the heat transferred from the system in step III should be to a reservoir at Tc. From Table 2, we see that the efficiency of a Carnot cycle engine is... 

As a whole, the Carnot cycle is found to consist of a mediator loop shown in Fig. 30 (a) and a multicoupler system composed of a net work sink as an overall target and the two couplers a heat source at high temperature and a heat sink at low temperature, as shown in Fig. 30 (b). Hence the mediators act as carrier of energy and entropy. 

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