Adiabatic compression-expansion

Vurzel and Polak (55) carried out extensive kinetic studies of the reduction of silicon tetrachloride to silicon in plasma devices. They first decomposed SiCl4 to SiCls in an adiabatic compression-expansion device and then completed the reduction in an RF plasma. They claimed that the decomposition of SiCl4 to silicon proceeded by a two-stage mechanism of chlorine atom removal ... 

The thermal efficiency of the process (QE) should be compared with a thermodynamically ideal Carnot cycle, which can be done by comparing the respective indicator diagrams. These show the variation of temperamre, volume and pressure in the combustion chamber during the operating cycle. In the Carnot cycle one mole of gas is subjected to alternate isothermal and adiabatic compression or expansion at two temperatures. By die first law of thermodynamics the isothermal work done on (compression) or by the gas (expansion) is accompanied by the absorption or evolution of heat (Figure 2.2). 

In adiabatic compression or expansion, no release or gain of heat by the gas occurs, and no change occurs in entropy. This condition is also known as isentropic and is typical of most compression steps. Actual conditions often cause a realistic deviation, but usually these are not sufficiently great to make the calculations in error. Table 12-4 gives representative average k values for a few common gases and vapors. 

Figures 12-37F and 12-37G use adiabatic compression and expansion (zero heat transfer). All heat added to the cycle comes from heating the engine exhaust by Heat rejected from the cycle, Qni> leaves through the aftercooler.

Adiabatic expansion of the air in the engine causes a maximum temperature drop of the exhaust. Adiabatic compression causes a maximum temperature rise of the compressed air. These effects combine to cause the greatest work loss of any compressed-air system, when pressurized air must be cooled back to atmospheric temperature. The energy analysis parallels the one just made for the polytropic system. This shows that net areas on both PV and TS graphs measure the work lost. 

Ideal Gases.—The state of unit mass of an ideal gas, undergoing adiabatic compression or expansion, is completely defined by the equations... 

For an irreversible process it may not be possible to express the relation between pressure and volume as a continuous mathematical function though, by choosing a suitable value for the constant k, an equation of the form Pv = constant may be used over a limited range of conditions. Equation 2.73 may then be used for the evaluation of / 2 v dP. It may be noted that, for an irreversible process, k will have different values for compression and expansion under otherwise similar conditions. Thus, for the irreversible adiabatic compression of a gas, k will be greater than y, and for the corresponding expansion k will be less than y. This means that more energy has to be put into an irreversible compression than will be received back when the gas expands to its original condition. 

GASEQ A Chemical Equilibrium Program for Windows. GASEQ is a PC-based equilibrium program written by C. Morley that can solve several different types of problems including composition at a defined temperature and pressure, adiabatic temperature and composition at constant pressure, composition at a defined temperature and at constant volume, adiabatic temperature and composition at constant volume, adiabatic compression and expansion, equilibrium constant calculations, and shock calculations. More information can found at the website http //www.arcl02.dsl.pipex.com/gseqmain.htm. 

In Step II, a drop in temperature occurs in the adiabatic reversible expansion, but no change in entropy occurs. The isentropic nature of II is emphasized by the vertical line. Step III is an isothermal reversible compression, with a heat numerically equal to Qi being evolved. As this step is reversible and isothermal, we have from Equation (6.53)... 

A (reversible) Joule cycle consists of the following four steps isobaric increase in volume, adiabatic expansion, isobaric decrease in volume, and adiabatic compression. Helium gas, with the equation of state... 

A reversible cycle also can be completed in three steps, such as isothermal expansion (at from V to V2, cooling (at constant V2) from 2 to Ti, and adiabatic compression back to the initial state. 

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... 

Here V is the crystal volume, k-p and ks are the isothermal and adiabatic compressibility (i.e., the contraction under pressure), P is the expansivity (expansion/contraction with temperature), Cp and Cv are heat capacities, and 0e,d are the Einstein or Debye Temperatures. Because P is only weakly temperature dependent,... 

Figure 4.3 Reversible Camot cycle, showing steps (1) reversible isothermal expansion at th (2) reversible adiabatic expansion and cooling from th to tc (3) reversible isothermal compression at tc (4) reversible adiabatic compression and heating back to the original starting point. The total area of the Camot cycle, P dV, is the net useful work w performed in the cyclic process (see text).

CARNOT CYCLE. An ideal cycle or four reversible changes in the physical condition of a substance, useful in thermodynamic theory. Starting with specified values of die variable temperature, specific volume, and pressure, the substance undergoes, in succession, an isothermal (constant temperature) expansion, an adiabatic expansion (see also Adiabatic Process), and an isothermal compression to such a point that a further adiabatic compression will return the substance to its original condition. These changes are represented on the volume-pressure diagram respectively by ub. he. ctl. and da in Fig. I. Or the cycle may he reversed ad c h a. 

Theoretical predictions for the isothermal compressibility can obviously be obtained from any theory of the equation of state. If, in addition, data for the specific heat are supplied, the adiabatic compressibility can be derived in the same way. Thus the compressibility can be derived from the vinual expansion of the equation of stale which expresses the ratio PV/RT in a power series in the density, the coefficients being related to the interactions of groups of two, three, etc., particles. 

The expansion of an ideal gas in the Joule experiment will be used as a simple example. Consider a quantity of an ideal gas confined in a flask at a given temperature and pressure. This flask is connected through a valve to another flask, which is evacuated. The two flasks are surrounded by an adiabatic envelope and, because the walls of the flasks are rigid, the system is isolated. We now allow the gas to expand irreversibly into the evacuated flask. For an ideal gas the temperature remains the same. Thus, the expansion is isothermal as well as adiabatic. We can return the system to its original state by carrying out an isothermal reversible compression. Here we use a work reservoir to compress the gas and a heat reservoir to remove heat from the gas. As we have seen before, a quantity of heat equal to the work done on the gas must be transferred from the gas to the heat reservoir. In so doing, the value of the entropy function of the heat reservoir is increased. Consequently, the value of the entropy function of the gas increased during the adiabatic irreversible expansion of gas. 

In Fig. 8, step I is an isothermal expansion, step II is an adiabatic expansion, step III is an isothermal compression, and step IV is an adiabatic compression. Note that zero heat is transferred in the adiabatic expansion and compression (steps II and IV) that we have added to complete the cycle, and that the work terms in these two steps exactly cancel, being equal to TC Cv dT in the expansion and Th Cv dT in the compression. (The work in an adiabatic... 

The temperature [K] and pressure [atm] of the input and output streams are specified following the mark . The adiabatic nature of this process is disclosed by the value of AH. The exergy destruction ToEASi is, therefore, given by changing sign of the exergy increase of this adiabatic process. Adiabatic compression and expansion are other examples of the singular system. 

If the change described in Exercise 1.19.13 is carried out in two stages, (a) an adiabatic compression to 50°C using a constant external pressure of 18.1 atm, and (b) an isothermal expansion against a constant external pressure of 2.0 atm, find AE, AH, W, and Q for each stage and also for the overall process. Compare the overall values with those of Exercise 1.19.14. Why is Q AH in (a), even though Pex was constant ... 

If the velocity of the reaction becomes fast enough and the reaction is sufficiently exothermic, the adiabatic expansion of our reacting zone will occur at a linear rate comparable with the velocity of sound. Under such circumstances a sharp pressure wave begins to be built up ahead of the reaction zone, and it can propagate as a shock wave of supersonic velocity in the unburned gases.As the shock front passes through the reaction mixture, it produces adiabatic compression. If the temperature in this adiabatically compressed zone behind the shock wave exceeds the... 

The change of temperature on adiabatic compression or expansion is measured, and the coefficient of expansion is generally known. It should be noted, however, that Cp is a function of pressure, so that only fairly small pressure differences can be used. It is usually sufficient to take (dr/dp) as equal to ATjAp)q, with finite differences. The specific heat may be calculated by the thermodynamic equation (12), 44.11, Cp=—T d GI6T )p, where G is the available energy. 1... 

Hirn demonstrated that saturated steam when expand adiabatically in a cylindrical copper vessel with plate-glass ends deposits droplets of liquid, visible as a fog. Cazin connected the cylinder with another containing a piston, so that the vapour could be adiabatically compressed as well as expanded. Steam and carbon disulphide vapours (or"<0), condensed on expansion, but ether vapour (or">0) on compression. The inversion temperatures for benzene and cUoroform were about 120° and 127°C. respectively, agreeing with those calculated from Regnaulfs results, for CS2 790°, ether — 113°, CHCl3 123-5°, benzene 100° C. 

Adiabatic compression until the temperature rises from Tc to Tfj. Isothermal expansion to arbitrary point c with absorption of heat < h1. 

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