Adiabatic expansion defined

Points a and b in Figure 6.7 represent the initial and final states of an irreversible adiabatic expansion of an ideal gas. The path between is not represented because the temperature has no well-defined value in such a change different parts of the system may have different temperatures. The inhomogeneities in the system that develop during the irreversible change do not disappear until a new equilibrium is reached at b. 

Absolute humidity is usually expressed in grunts of water vapor per cubic meter or. in engineering practice, in grains per cubic foot. Because this measure ol atmospheric humidity is nol conservative with respect in adiabatic expansion or compression, it is noi commonly used hy mcieorologisis. As occasionally used in air-conditioning practice, absolute humidity refers to the number of grains of water vapor per pound of tuoisl air. which is dimensionally identical with the specific humidity t defined below I. 

The significance of the change in polytropic exponent with efficiency is brought out more clearly if we take the mth root of both sides of equation (14.22) to restate the equation defining the frictionally resisted, adiabatic expansion in the alternative form ... 

Dropwise condensation of a vapor diluted in a carrier gas occurs whenever the vapor becomes supersaturated due to a change of state of the gas/vapor mixture. By supersaturation we define the actual vapor pressure over the equilibrium vapor pressure (over a flat surface) at the same temperature. The change of state may be an adiabatic expansion as in cloud chambers, supersonic nozzles and shock tubes or a diffusion process as in diffusion cloud chambers [1]. 

The potential temperatnre is defined as the temperature resulting when dry air is brought adiabatically from its initial state to a standard pressure of 1000 mb (mb = millibar). For an adiabatic expansion of an ideal gas ... 

Reversible adiabatic expansion. In this step, q = 0, but because it is expansion, work is done by the engine. The work is defined as W2. 

The Carnot cycle is defined as having a certain specific first step, the isothermal expansion of a gas. Can a Carnot cycle start at step 2, the adiabatic expansion Why or why not Hint See Figure 3.2.)... 

Adiabatic energy transfer occurs when relative collision velocities are small. In this case the relative motion may be considered a perturbation on adiabatic states defined at each intermolecular position. Perturbed rotational states have been introduced for T-R transfer at low collision energies and for systems of interest in astrophysics.A rotational-orbital adiabatic basis expansion has also been employed in T-R transfer,as a way of decreasing the size of the bases required in close-coupling calculations. In T-V transfer, adiabatic-diabatic transformations, similar to the one in electronic structure studies, have been implemented for collinear models.Two contributions on T-(R,V) transfer have developed an adiabatical semiclassical perturbation theory and an adiabatic exponential distorted-wave approximation. Finally, an adiabati-cally corrected sudden approximation has been applied to RA-T-Rg transfer in diatom-diatom collisions. 

This makes it desirable to define other representations in addition to the electronically adiabatic one [Eqs. (9)-(12)], in which the adiabatic electronic wave function basis set used in the Bom-Huang expansion (12) is replaced by another basis set of functions of the electronic coordinates. Such a different electronic basis set can be chosen so as to minimize the above mentioned gradient term. This term can initially be neglected in the solution of the / -electionic-state nuclear motion Schrodinger equation and reintroduced later using perturbative or other methods, if desired. This new basis set of electronic wave functions can also be made to depend parametrically, like their adiabatic counterparts, on the internal nuclear coordinates q that were defined after Eq. (8). This new electronic basis set is henceforth refened to as diabatic and, as is obvious, leads to an electronically diabatic representation that is not unique unlike the adiabatic one, which is unique by definition. 

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

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. 

This is referred as BO ansatz. This ansatz is taken as a variational trial function. Terms beyond the leading order in m/M are neglected m is the electronic and M is nuclear mass, respectively). The problem with expansion (4) is that functions /(r, R) contain except bound states also continuum function since it includes the centre of mass (COM) motion. Variation principle does not apply to continuum states. To avoid this problem we can separate COM motion. The remaining Hamiltonian for the relative motion of nuclei and electrons has then bound state solution. But there is a problem, because this separation mixes electronic with nuclear coordinates and also there is a question how to define molecule-fixed coordinate system. This is in detail discussed by Sutcliffe [5]. In the recent paper by Kutzelnigg [8] this problem is also discussed and it is shown how to derive adiabatic corrections using, as he called it, the Bom-Handy ansatz. There are few important steps to arrive at formula for a diabatic corrections. Firstly, one separates off COM motion. Secondly, (very important step) one does not specify the relative coordinates (which are to some extent arbitrary). In this way one arrives at relative Hamiltonian Hrd [8] with trial wavefunction If we make BO ansatz... 

The shaft work given by Eq. (7.27) is the maximum that can be obtained from an adiabatic turbine with given inlet conditions and given discharge pressure. Actual turbines produce less work, because the actual expansion process is irreversible. We therefore define a turbine efficiency as... 

Of course, this corresponds to an adiabatic potential-energy surface with two potential-energy minima separated by a well-defined barrier. Note that y A contains anharmonicities induced into Xr by D/A interactions as well as energy corrections that originate from D/A coupling. To some extent (i.e., as in first-order perturbation theory or in a Taylor s series expansion around the diabatic values of... 

This isothermal bulk modulus (Kj) measured by static compression differs slightly from the aforementioned adiabatic bulk modulus (X5) defining seismic velocities in that the former (Kj) describes resistance to compression at constant temperature, such as is the case in a laboratory device in which a sample is slowly compressed in contact with a large thermal reservoir such as the atmosphere. The latter (X5), alternatively describes resistance to compression under adiabatic conditions, such as those pertaining when passage of a seismic wave causes compression (and relaxation) on a time-scale that is short compared to that of thermal conduction. Thus, the adiabatic bulk modulus generally exceeds the isothermal value (usually by a few percent), because it is more difihcult to compress a material whose temperature rises upon compression than one which is allowed to conduct away any such excess heat, as described by a simple multiplicative factor Kg = Kp(l + Tay), where a is the volumetric coefficient of thermal expansion and y is the thermodynamic Griineisen parameter. 

The expansion factor is defined as the molar density of the reagents divided by the molar density of the products in an explosive mixture. The expansion factor is a measure of the increase in volume resulting from combustion. The maximum value of the expansion factor is for adiabatic combustion. 

Here the transformation angle depends on R. 0 and y. Since there is no coupling between the H,> state, of A reflection symmetry, with the ni> and 2> states, of A reflection symmetry, the adiabatic and diabatic states of A reflection symmetry are identical. Alternatively, we can define the diabatic states in terms of signed-A, rather than Cartesian, projections, namely Hi>, H i>, and 2>. These signed-A states are those which we used above in the expansion of the scattering wavefiinction. Note that the state we designate as E corresponds to A = 0. 

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