Heat and work reservoirs

We define a heat reservoir as any body, used as part of the surroundings of a particular system, whose only interaction with the system is across a diathermic boundary. A heat reservoir is then used to transfer heat to or from a thermodynamic system and to measure these quantities of heat. It may consist of one or more substances in one or more states of aggregation. In most cases a heat reservoir must be of such a nature that the addition of any finite amount of heat to the system or the removal of any finite amount of heat from the system causes only an infinitesimal change in the temperature of the reservoir. 

A work reservoir is similarly defined as any body or combination of bodies, used as part of the surroundings, whose only interaction with the system is one that may be described in terms of work. We may have a different type of reservoir for each mode of interaction other than thermal interaction. A work reservoir then is used to perform work across the boundary separating the reservoir and the thermodynamic system and to measure these quantities of work. In the following we are, in order to simplify the discussion, primarily concerned with mechanical work, but this limitation does not alter or limit the basic concepts. A reservoir for mechanical work may be a set of weights and pulleys in a gravitational field, an idealized spring, or a compressible fluid in a piston-and-cylinder arrangement. In any case the reservoir must 

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The objective here is to show that the reaction equilibrium criteria (7.6.3) are a consequence of the more general equilibrium criterion (7.1.40) that applies to any NPT system, including reacting systems. Consider a system of C species confined to a closed vessel and maintained at constant T and P by contact with an external heat and work reservoir. The species may undergo 51 independent chemical reactions. Since T and P are fixed for the entire system, the NPT criterion for equilibrium (7.1.40) applies that is, when all reactions are complete and equilibrium is reached, the system s total Gibbs energy will be a minimum,... 

The longer story, of course, involves electronic messages, thermal collisions, and adjustments of the system composition. This is the subject of Figure 7.1, which represents in schematic terms a gas coupled to heat and work reservoirs. For discussion purposes, let the container be leak-proof and held at constant temperature and pressure. Let the system be composed only of A initially as rq)resented by the open circles. Let one of the A molecules be poised for conversion to B, the latter represented by the filled circle. 

FIGURE 7.1 A chemically reactive gas coupled to heat and work reservoirs. A molecules are represented by the open circles. A single A is poised for conversion to B, the latter represented by the filled circle. 

Figure 5.6 An isolated system composed of subsystem A (the one we will eventually designate as the system) and subsystem B (the surroundings containing a heat reservoir). Heat and work will be exchanged until TA = 7b, pA = p%, and equilibrium is established.

Beginning with the industrial revolution, great improvements in standards of living have been achieved by the use of thermal devices, which interconvert heat and work. Three such devices, which operate with two heat reservoirs, are shown in Fig. 3. For each, the efficiency, e, is defined as the amount of the type of energy desired divided by the amount of energy that is expended in obtaining it. 

Since the mass of the system is fixed, the state can be described by any two of the three variables T, p, V. A system of this sort that produces only heat and work effects in the surroundings is called a heat engine. A heat reservoir is a system that has the same temperature everywhere within it this temperature is unaffected by the transfer of any desired quantity of heat into or out of the reservoir. 

It is well known from thermodynamic principles that energy transferred as work is more useful than energy transferred as heat. Work can be completely converted to heat, but only a fraction of heat can be converted to work. Furthermore, as the temperature of a system is decreased, heat transferred from the system becomes less useful and less of the heat can be converted to work. A state property that accounts for the differences between heat and work is entropy, S. When heat is transferred into a closed system at temperature T, the entropy of the system increases because entropy transfer accompanies heat transfer. By contrast, work transfer (shaft work) is not accompanied by entropy transfer. When heat is transferred at a rate Q from a surrounding heat reservoir at a constant temperature, Treservoir, into a system, the heat reservoir experiences a decrease in entropy given by... 

During each stage of the experimental process with nonzero heat, we allow the Carnot engine to undergo many infinitesimal Carnot cycles with infinitesimal quantities of heat and work. In one of the isothermal steps of each Carnot cycle, the Carnot engine is in thermal contact with the heat reservoir, as depicted in Fig. 4.8(a). In this step the Carnot engine has the same temperature as the heat reservoir, and reversibly exchanges heat dg with it. 

We shall now prove that P, for fixed values of 7r and the temperature, is definite for a given solution. For this purpose we have first of all to show that the dilution or concentration of the solution can be effected isothermally and reversibly. If the above apparatus is constructed of some good conductor of heat, placed in a large constant-temperature reservoir, and if all processes are carried out very slowly, the isothermal condition is satisfied. Further, suppose the end pistons fixed, and then apply to the septum an additional small pressure SP towards the solution. There will be a slight motion of the septum, through a small volume SV, and work... 

It is impossible to construct a device which, operating in a cycle, will produce no other effect than the extraction of heat from a reservoir and the performance of an equivalent amount of work. 

To derive the condition for thermodynamic equilibrium, we start with an isolated system consisting of two subsystems as shown in Figure 5.6. Subsystem A is the one of primary interest in that it is the one in which the chemical process is occurring. Subsystem B is a reservoir in contact with subsystem A in such a way that energy in the form of heat or work can flow between the two subsystems. If left alone, the system will come to equilibrium. Energy will be transferred between the subsystems so that the temperature and pressure will be... 

Two classically important statements have been provided. The first statement, due to Lord Kelvin, is that it is not possible by a cyclic process to take heat from a reservoir and convert it into work without at the same time transferring heat from a hot to a cold reservoir. This statement of the second law is related to equilibria when it is realized that work can be obtained from a system only when the system is not already at equilibrium. The statement recognizes that the spontaneous process is the flow of heat from a higher to a lower temperature and that only from such a spontaneous process can the work be acquired. The second important classic statement, due to Clausius, is that it is not possible to transfer heat from a cold to a hot reservoir without at the same time converting a certain amount of work into heat. The operation of a refrigerator readily illustrates this statement... 

The second law of thermodynamics, as formulated by Kelvin, states that no process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work in other words, in any natural process involving a transfer of energy, some energy is converted irreversibly into heat that cannot be involved in further exchange. The second law of thermodynamics, therefore, is a recognition of spontaneous and nonspontaneous processes and the fact that natural processes have a sense of direction. 

The efficiency of the Carnot heat engine operating between a fixed high-temperature heat source thermal reservoir at Th and a fixed low-temperature heat sink thermal reservoir at Tl is irrespective of the working substance. 

Figure 4.2 Schematic engine (as envisioned by Carnot), consisting of a working fluid that absorbs heat qh from a hot reservoir (temperature th) and expels a smaller quantity of heat qc to a cold reservoir (temperature tc), with performance of work w (= qh — qc ) on the surroundings. Arrows denote the magnitude and direction of heat or work flow.

We return to the piston-and-cylinder arrangement discussed in Section 2.3. In that discussion we did not completely describe the process because we were interested only in developing the concept of work. Here, to complete the description, we choose an isothermal process and a gas to be the fluid. We then have a gas confined in the piston-and-cylinder arrangement. A work reservoir is used to exert the external force, Fe, on the piston this reservoir can have work done on it by the expansion of the gas or it can do work by compressing the gas. A heat reservoir is used to make the process isothermal. The piston is considered as part of the surroundings, so the lower surface of the piston constitutes part of the boundary between the system and its surroundings. Thus, the piston, the cylinder, and the two reservoirs constitute the surroundings. 

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