Reversible adiabatic change processes

Theorem. From any state of a system, the maximum energy that can be extracted adiabatically in a CCP process is the work done in a reversible adiabatic process that ends in a stable equilibrium state. Moreover, the energy change of a system starting from a given state and ending at a stable equilibrium state is the same for all reversible adiabatic CCP processes. We call this energy the adiabatic availability. 

Obviously die first law is not all there is to the structure of themiodynamics, since some adiabatic changes occur spontaneously while the reverse process never occurs. An aspect of the second law is that a state fimction, the entropy S, is found that increases in a spontaneous adiabatic process and remains unchanged in a reversible adiabatic process it caimot decrease in any adiabatic process. 

Isentropic A reversible adiabatic process, in which there is no change in the entropy of the system. 

Besides the reversible and irreversible processes, there are other processes. Changes implemented at constant pressure are called isobaric process, while those occurring at constant temperature are known as isothermal processes. When a process is carried out under such conditions that heat can neither leave the system nor enter it, one has what is called an adiabatic process. A vacuum flask provides an excellent example a practical adiabatic wall. When a system, after going through a number of changes, reverts to its initial state, it is said to have passed through a cyclic process. 

In a system undergoing a reversible adiabatic process, there is no change in its entropy. This is so because by definition, no heat is absorbed in such a process. A reversible adiabatic process, therefore, proceeds at constant entropy and may be described as isentropic. The entropy, however, is not constant in an irreversible adiabatic process. 

The entropy, Spontaneous vs non-spontaneous, Reversible and irreversible processes, Calculation of entropy changes (Isothermal, isobaric, isochoric, adiabatic), Phase changes at equilibrium, Trouton s rule, Calculation for irreversible processes... 

One mole of an ideal gas, CP = (7/2)R and Cv = (5/2)R, is compressed adiabatically in a piston/cylinder device from 1 bar and 40°C to 4 bar. The process is irreversible and requires 30 percent more work than a reversible, adiabatic compression from the same initial state to the same final pressure. What is the entropy change of the gas7... 

Microcalorimeters are well suited for the determination of differential enthalpies of adsorption, as will be commented on in Sections 3.2.2 and 3.3.3. Nevertheless, one should appreciate that there is a big step between the measurement of a heat of adsorption and the determination of a meaningful energy or enthalpy of adsorption. The measured heat depends on the experimental conditions (e.g. on the extent of reversibility of the process, the dead volume of the calorimetric cell and the isothermal or adiabatic operation of the calorimeter). It is therefore essential to devise the calorimetric experiment in such a way that it is the change of state which is assessed and not the mode of operation of the calorimeter. 

Consider now an irreversible process in a closed system wherein no heat transfer occurs. Such a process is represented on the P V diagram of Fig. 5.6, which shows an irreversible, adiabatic expansion of 1 mol of fluid from an initial equilibrium state at point A to a final equilibrium state at pointB. Now suppose the fluid is restored to its initial state by a reversible process consisting of two steps first, the reversible, adiabatic (constant-entropy) compression of tile fluid to tile initial pressure, and second, a reversible, constant-pressure step that restores tile initial volume. If tlie initial process results in an entropy change of tlie fluid, tlien tliere must be heat transfer during tlie reversible, constant-P second step such tliat ... 

The change in volume of a gas again illustrates the difference between reversible and irreversible processes. The adiabatic compression of a gas (see p. 91) is reversible, as the initial state may be re-estabhshed completely by an adiabatic expansion. In practice, however, it is impossible to construct vessels absolutely impermeable to heat. No actual compression is therefore strictly adiabatic, as some of the heat produced is always lost by conduction or radiation to the surroundings. The less the permeability of the walls of the vessel, the smaller this loss in heat will be, and the more nearly will the change in volume approximate to a reversible process. 

For a thermodynamically reversible adiabatic process Tgys = Tsmr) at constant pressure, the change in entropy of the surroundings can be expressed as [11] ... 

Reversible adiabatic compression in which the gas temperature changes from T, the temperature of the cold reservoir, to T, the temperature of the hot reservoir. Since this is an adiabatic process, dQ = 0, and, from the first law, -dW = dU. The work done on the gas in this step is, therefore,... 

By measuring the temperature change and the specific volume change accompanying a small pressure change in a reversible adiabatic process, one can evaluate the derivative... 

Figure 2.8 Schematic plot of states accessible via adiabatic processes in closed systems. From the initial state 1 only states on the line can be reached by reversible adiabatic volume changes. States above the reversible adiabat can be reached only by processes that include irreversible adiabatic volume changes. States below the reversible adiabat cannot be reached by any adiabatic volume change.

Isentropic process Any process that takes place without a change of entropy. The quantity of heat transferred, 5Q, in a reversible process is proportional to the change in entropy, 5S, i.e. 5Q= 7SS, where T is the thermodynamic temperature. Therefore, a reversible adiabatic process is isentropic, i.e. when 5Q equals zero, 5S also equals zero. 

The temperature-entropy diagram in fig. 1 clearly shows that fluids of low molar specific heat, e.g. water, can only partly be evaporated or condensed by reversible adiabatic processes. Fluids of high molar specific heat, e.g. perfluoro-n-hexane (C6F14), however, make complete adiabatic phase changes feasible. Physically, the difference between... 

The maximum flow is obtained for the reversible adiabatic, that is, isentropic state change. However, for the calculation of this process, the speed of sound has to be evaluated at the conditions in the cross-flow area (index 1) of the valve. For this purpose, an iterative procedure is necessary. The necessary steps are as follows ... 

While the entropy change is zero for either system during the reversible adiabatic steps (see Rgures 9.12c and 9.13c), it must be emphasized that the entropy change is greater than zero for an irreversible adiabatic process. An example for an elastomer is letting go of a stretched rubber band. 

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