Heating reversible

The definition of the heat capacity C of a closed system is given by Eq. 3.1.7 on page 63  

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Heat pump A reversed heat engine or refrigerator that takes in heat from a body at low temperature and by the expenditure of mechanical work rejects heat to a body at a higher temperature. 

Reversible heat engine A heat engine, which will convert a certain quantity of heat into an amount of work (W7), that will produce the original quantity of heat if the same amount of w ork is expended in driving the engine backwards. 

Consider first the steady flow of fluid through a control volume CV between prescribed stable states X and Y (Fig. 2.1) in the presence of an environment at ambient temperature Tj, (i.e. with reversible heat transfer to that environment only). The maximum work which is obtained in reversible flow between X and Y is given by... 

Fig. 2.3 shows such a fully reversible steady flow through the control volume CV. The heat transferred [GrevIx. supplies a reversible heat engine, delivering external work [( c)rev]x and rejecting heat [(2o)rev1x to the environment. 

The reversible reaction heat of the cell is defined as the reaction entropy multiplied by the temperature [Eq. (15)]. For an electrochemical cell it is also called the Peltier effect and can be described as the difference between the reaction enthalpy AH and the reaction free energy AG. If the difference between the reaction free energy AG and the reaction enthalpy AH is below zero, the cell becomes warmer. On the other hand, for a difference larger than zero, it cools down. The reversible heat W of the electrochemical cell is therefore ... 

The relation between reaction free energy, temperature, cell voltage, and reversible heat in a galvanic cell is reflected by the Gibbs-Helmholtz equation [Eq. (31)]. 

Besides the reversible production of heat at the junctions, there is an evolution of heat all round the circuit due to frictional resistance, this Joule s heat being proportional to the square of the current, and hence not reversed with the latter. There is also a passage of heat by conduction from the hotter to the colder parts. But if the current strength is reduced, the Joule s heat, being proportional to its square, becomes less and less in comparison with the Peltier heat, and with very small currents is negligible. We shall further assume that the reversible thermoelectric phenomena proceed independently of the heat conduction, so that the whole circuit may be treated as a reversible heat... 

We first assume that the Peltier effects are the only reversible heat effects in the circuit. Then if 7Ti, 7t2 are the Peltier effects at the hot and cold junctions ... 

Thus, we can conclude that, within the neighborhood of every state in this thermodynamic system, there are states that cannot be reached via adiabatic paths. Given the existence of these states, then, the existence of an integrating denominator for the differential element of reversible heat, Sqrev, is guaranteed from Caratheodory s theorem. Our next task is to identify this integrating denominator. 

Calculate the entropy change for reversible heat transfer (Example 7.1). 

Distributed water loop heat Central reversing heat pump... 

Outdoor air is treated and supphed by a central air-handling unit. The required amount of air is delivered into the return air plenum of the fan coil units. The air-handling unit is provided with a hot water coil and chilled water coil. Both the coils are served by central reversing heat pump. A total enthalpy wheel can reduce the energy consumed for treating outdoor air. 

Assuming thermodynamic reversibility of the cell reaction and with the help of eqs 1 and 3, we can obtain the reversible heat effect. 

A process is thermodynamically reversible when an infinitesimal reversal in a driving force causes the process to reverse its direction. Since all actual processes occur at finite rates, they cannot proceed with strict thermodynamic reversibility and thus additional nonrevers-ible effects have to be regarded. In this case, under practical operation conditions, voltage losses at internal resistances in the cell (these kinetic effects are discussed below) lead to the irreversible heat production (so-called Joule heat) in addition to the thermodynamic reversible heat effect. 

Among the three heat-generation terms, the irreversible and reversible heat sources of ORR are dominant. For a straight-channel cell shown in Figure 12, the total amount of heat release is 2.57 W, of which the irreversible heat is 55.3%, the reversible heat 35.4%, and the Joule heat only 9.3% The total heat released from the fuel cell can also be estimated from the overall energy balance, i.e. 

All reversible heat engines operating between a fixed high-temperature heat source thermal reservoir and a fixed low-temperature heat sink thermal reservoir have the same efficiency. 

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