Equilibria thermal equilibrium

The. Homogeneous Equilibrium Model (HEM) assumes uniform mixing of the phases across the. pipe diameter, no phase slip (mechanical equilibrium), thermal equilibrium between, the..phases and complete vapour/ liquid, equilibrium. "Homogenous" in the context of the HEM refers to the flow in the vent line. 

Equilibrium in a multiphase system implies thermal, mechanical, and material equilibrium. Thermal equilibrium requires uniformity of temperature throughout the system, and mechanical equilibrium requires uniformity of pressure. To find the criterion for material equilibrium, we treat a two-phase system and consider a transfer of dn moles from phase p to phase a. First, we regard each phase as a separate system. Because material enters or leaves these phases, they are open systems and we must use Eq. (4) to write their change in internal energy ... 

If the phases in a multiphase simple system of p phases and c components are separated from each other so that they cannot equilibrate, there are c + 1 independent intensive variables for each phase, a total of p c + 1) variables. Now place the phases in contact with each other, open them to each other, and allow them to equilibrate. There are three aspects of equilibrium. Thermal equilibrium implies that all phases have the same temperature, mechanical equilibrium implies that all phases have the same pressure, and phase equilibrium implies that the chemical potential of every substance has the same value in every phase. 

Equation (A2.1.1) is essentially an expression of the concept of thermal equilibrium. Note, however, that, in this fominlation, this concept precedes the notion of temperature. 

The concept of temperature derives from a fact of conmron experience, sometimes called the zeroth law of themiodynamics , namely, if tM o systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. To clarify this point, consider the tliree systems shown schematically in figure A2.1.1, in which there are diathemiic walls between systems a and y and between systems p and y, but an adiabatic wall between systems a and p. 

B1.15.2.2 THERMAL EQUILIBRIUM, MAGNETIC RELAXATION AND LORENTZIAN UNESHAPE... 

The initial conditions of system (20) coincide with those for the original equations X/,(0) = X" and V/i(0) = V . Appropriate treatments, as discussed in [72], are essential for the random force at large timesteps to maintain thermal equilibrium since the discretization S(t — t ) => 6nml t is poor for large At. This problem is alleviated by the numerical approach below because the relevant discretization of the Dirac function is the inner timestep At rather than a large At. 

As stated earlier, within C(t) there is also an equilibrium average over translational motion of the molecules. For a gas-phase sample undergoing random collisions and at thermal equilibrium, this average is characterized by the well known Maxwell-Boltzmann velocity distribution ... 

Standardizing the Method Equation 10.34 shows that emission intensity is proportional to the population of the excited state, N, from which the emission line originates. If the emission source is in thermal equilibrium, then the excited state population is proportional to the total population of analyte atoms, N, through the Boltzmann distribution (equation 10.35). 

Depending on the method of pumping, the population of may be achieved by — Sq or S2 — Sq absorption processes, labelled 1 and 2 in Figure 9.18, or both. Following either process collisional relaxation to the lower vibrational levels of is rapid by process 3 or 4 for example the vibrational-rotational relaxation of process 3 takes of the order of 10 ps. Following relaxation the distribution among the levels of is that corresponding to thermal equilibrium, that is, there is a Boltzmann population (Equation 2.11). 

Fig. 2. (a) A schematic diagram of a n—p junction, including the charge distribution around the junction, where 0 represents the donor ion 0, acceptor ion , electron °, hole, (b) A simplified electron energy band diagram for a n—p junction cell in the dark and in thermal equilibrium under short-circuit... 

Doppler broadening arises from the random thermal agitation of the active systems, each of which, in its own test frame, sees the appHed light field at a different frequency. When averaged over a Maxwellian velocity distribution, ie, assuming noninteracting species in thermal equilibrium, this yields a line width (fwhm) in cm C... 

Alkylthiothiazoles rearrange thermally into the 3-alkylthiazoline-2-thiones in the imidazole series a thermal equilibrium is reached. 

Nitrone (530) exists in thermal equilibrium with vinylamine (531) and isoxazolidine (532), with (532) (a dimer of 530 and 531) being predominant. The equilibrium in DMSO was studied by and NMR spectra (80TL3447). 

Even iV-aryldiaziridines can be obtained. Compound (274) is formed on irradiation of its 1,3-dipolar isomer, which is in thermal equilibrium with its head-to-tail dimer (82TH50800). 

Penicillin sulfoxides can be epimerized by heat to afford thermal equilibrium mixtures of a- and /3-sulfoxides, the position of the equilibrium depending on the C(6) side chain (Scheme 5). Deuterium incorporation studies support a sulfenic acid, e.g. (18), as the intermediate in these transformations. This mechanism is also supported by the finding that when an a-sulfoxide epimerizes to a /3-sulfoxide there is a simultaneous epimerization at C(2) (71JCS(C)3540). With irradiation by UV light it is possible to convert a more thermodynamically stable /3-sulfoxide to the a-sulfoxide (69JA1530). 

Critical Temperature The critical temperature of a compound is the temperature above which a hquid phase cannot be formed, no matter what the pressure on the system. The critical temperature is important in determining the phase boundaries of any compound and is a required input parameter for most phase equilibrium thermal property or volumetric property calculations using analytic equations of state or the theorem of corresponding states. Critical temperatures are predicted by various empirical methods according to the type of compound or mixture being considered. 

The period after which this can be repeated will depend upon the heating curve and the thermal time constant of the motor, i.e. the time the motor will take to reach thermal equilibrium after repeated starts (See Chapter 3). 

The operation of a motor at a rated load may be for an unlimited period to reach thermal equilibrium (Figure 3.1) and possible applictilions are pumps, blowers, fans and compressors. 

This is a sequence of identical duly cycles, each consisting of a period of operation at constant load and a period of operation at no-load. The repeat load and no-load periods are just adequate to attain thermal equilibrium during one duly cycle. There is no rest and de-energizing period, (Figure 3.6). Unless otherwise specified, the duration of the duty cycle will be 10 minutes. 

This is the time taken by the stator or the rotor, whichever is less, to reach the limiting temperature rise, as specified in Table 7.5, when the starting current /s, is pas.sed through the stator windings after the motor has reached thermal equilibrium, underrated conditions. For increa.sed safety motors, this time should not be less than 5 seconds (preferably 10 seconds or more). 

In motors for periodic duty, the test should be continued until thermal equilibrium has been reached. Unless otherwise agreed, the duration of one cycle should be 10 minutes for the purpose of this test. Temperature measurements should be made at the end of a cycle to establish thermal equilibrium. 

When thermal equilibrium is reached, the motor must be stopped as quickly as possible. Measurements must be taken both while the motor was running and after shutdown (wherever possible). No corrections for observed temperatures are necessary if the stopping period does not exceed the values given in Table 11.2. 

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