Reversible work source

T0 compute the maximum work, we need tw o other idealizations. A reversible work source can change volume or perform work of any other kind quasi-statically, and is enclosed in an impermeable adiabatic waU, so 6g = TdS = 0 and dU = S w. A reversible heat source can exchange heat quasi-statically, and is enclosed in a rigid wall that is impermeable to matter but not to heat flow, so = pdV = 0 and dU = 6q = TdS. A reversible process is different from a reversible heat or work source. A reversible heat source need not have AS = 0. A reversible process refers to changes in a whole system, in w-hich a collection of reversible heat plus work sources has AS = 0. The frictionless weights on pulleys and inclined planes of Newtonian mechanics are reversible w ork sources, for example. The maximum possible work is achieved w hen reversible processes are performed with reversible heat and work sources. 

Because a reversible work source is adiabatic, ASw = qwIT = 0, so... 

Figure 7.10 (a) In this idealized heat engine, a piston containing cooled gas starts at rest. When heat qn enters from the reversible heat source, the energies of the gas molecules increase, (b) Work is performed by the expansion of the heated gas (the reversible work source), extracting energies from the molecules, (c) Heat flows out from the reversible heat source and the volume in the piston decreases. 

The physical meaning of both entropies is now clear. Whereas Sp stands for the heat transferred by the system to the sources (Eq. (36)), the total dissipation term TS (Eq. (35)) is just the difference between the total mechanical work exerted on the system, W(r), and the reversible work, Wrev = AF. It is customary to define this quantity as the dissipated work, Waiss ... 

The fuel cell is the isothermal heat source of the Carnot cycle CC and delivers the reversible heat < FCrev The reversible work >vtccrev of CC is defined by... 

If the temperature T of a substance is lower than the temperature T0 of the environment, a heat engine can be operated between the environment (heat source) and the low temperature substance (heat sink). Let us consider a reversible heat engine as shown in Fig 10.4 in which the engine gas receives an amount of heat dQ from the environment at atmospheric temperature r0 and performs an amount of reversible work dWm releasing an amount of heat into the low temperature substance at temperature T, whose enthalpy is then increased by an amount dH =dQ- dWm > 0. From the efficiency of the reversible engine we have Eq. 10.18 ... 

General principles, representative applications, fluctuations and irreversible thermodynamics. Chapter 4 discusses quasistatic processes, reversible work and heat sources, and thermodynamic engines. 

Although weak fluorescence in the P— P lines was observed, from a practical standpoint only the P— P lines were found to be intense enough for resonance fluorescence work at low atom concentrations. The fluorescence count rates using the whole of the fully allowed P— P transition of F were typically 2 counts s" at [F] = 1 X 10 cm . These data set a lower concentration limit of 1 X 10 cm" for the smallest detectable concentration of F P atoms. Similar lower limits for O, Br, and I atoms are appreciably less, and are continually being improved by better attention to collimation and detection. Because of the low count rates observed in the F-atom resonance fluorescence studies, it is a better approach to use resonance absorption with a non-reversed line source (see above). 

Figure 7.9 Schematic diagram of heat and work sources in which the hot gas in an engine partly converts to work, and partly converts to colder exhaust gas. The ellipses indicate reversible heat and work sources. The arrows indicate processes. A physical realization is shown in Figure 7.10. 

Instead of calculations, practical work can be done with scale models (33). In any case, calculations should be checked wherever possible by experimental methods. Using a Monte Carlo method, for example, on a shape that was not measured experimentaUy, the sample size in the computation was aUowed to degrade in such a way that the results of the computation were inaccurate (see Fig. 8) (30,31). Reversing the computation or augmenting the sample size as the calculation proceeds can reveal or eliminate this source of error. 

We now place the cylinder on the source, and allow the working substance to expand reversibly and isothermally at Ti until any arbitrary quantity of heat Qi has been absorbed. 

From this we deduce the following important corollary If a quantity of heat Q is absorbed in a reversible cycle, with given temperatures of source and refrigerator, the quantity of work A obtained from it is independent of the arrangement used in performing the cycle. 

It is an immediate consequence of Carnot s theorem that the ratio of the quantities of heat absorbed and rejected by a perfectly reversible engine working in a complete cycle, depends only on the temperatures of the bodies which serve as source and refrigerator. 

Definition of Absolute Temperature.— The temperatures of two bodies are proportional to the quantities of heat respectively taken in and given out in localities at one temperature and at the other, respectively, by a material system subjected to a complete cycle of perfectly reversible thermodynamic operations, and not allowed to part with or take in heat at any other temperature or, the absolute values of two temperatures are to one another in the proportion of the heat taken in to the heat rejected in a perfect thermodynamic engine working with a source and refrigerator at the higher and lower of the temperatures respectively. ... 

We shall now define what is to be understood by equal intervals of temperature. Let us imagine that we have a system of reversible engines [1,2], [2,8], [8,4],. . . , working between constant temperature reservoirs (1), (2), (8), (4),. . . , so that the refrigerator of any engine (except the last) forms the source of the next engine. Let each perform a cycle so that... 

Hence the temperature of the refrigerator is zero when all the heat absorbed from the source is converted into work by the reversible engine. 

Theorem.—The work obtained from a given quantity of heat absorbed from the source by a reversible engine is the greatest amount which can possibly be obtained with given temperatures of source and refrigerator. 

Such a reversible cell may be used as a source of external work by attaching its poles to the two plates of an electrostatic air-condenser, or to an ideal electromotor. Slight motions of the parts of these systems in one direction or the other against the external forces holding them in equilibrium, will yield or absorb external work, and cause corresponding currents to pass round the system. 

---