System isolated system

Risk Reduction Factors Coutrol/ rator responses. Alarms, Control system response. Manual anti automatic ESD, Fire/gas detection system Sa/ety System Responses Relief valves. Depressurization system. Isolation systems, High reliability trips. Back-up systems... 

Any chemical, biological, or mechanical system in which both heat and matter within the system can be transferred to and from its surrounding environment. Thus, a change in the immediate environment can result in a change in the system under consideration. See also Closed System Isolated System... 

A term used in thermodynamics to designate a region separated from the rest of the universe by definite boundaries. The system is considered to be isolated if any change in the surroundings the portion of the universe outside of the boundaries of the system) does not cause any changes within the system. See Closed System Isolated System Open System... 

Isolated Systems Isolated systems exchange neither energy nor matter with the environment. The simplest example from chemical or biological engineering is the adiabatic batch reactor. Isolated systems naturally tend towards their thermodynamic equilibrium with time. This state is characterized by maximal entropy, or the highest possible degree of disorder. 

Explain the following terms thermochemistry, system, surroundings, open system, closed system, isolated system, exothermic process, endothermic process. 

We placed no restriction on whether or not work was done during this process, so we derived this relation for a closed, perfectly insulated system but not necessarily an isolated system. Isolated systems have adiabatically insulating walls as well, so evidently (5.6) applies in isolated systems as well as closed, adiabatic ones. 

Open system Closed system Isolated system ... 

Figure 1.1 Isolated, closed and open systems. Isolated systems exchange neither energy nor matter with the exterior. Closed systems exchange heat and mechanical energy but not matter with the exterior. Open systems exchange both energy and matter with the exterior.

This is frequently stated for an isolated system, but the same statement about an adiabatic system is broader.) A2.1.4.6 IRREVERSIBLE CHANGES AND THE MEASUREMENT OF ENTROPY... 

For example, the expansion of a gas requires the release of a pm holding a piston in place or the opening of a stopcock, while a chemical reaction can be initiated by mixing the reactants or by adding a catalyst. One often finds statements that at equilibrium in an isolated system (constant U, V, n), the entropy is maximized . Wliat does this mean ... 

Equation (A2.1.21) includes, as a special case, the statement dS > 0 for adiabatic processes (for which Dq = 0) and, a fortiori, the same statement about processes that may occur in an isolated system (Dq = T)w = 0). If the universe is an isolated system (an assumption that, however plausible, is not yet subject to experimental verification), the first and second laws lead to the famous statement of Clausius The energy of the universe is constant the entropy of the universe tends always toward a maximum. ... 

If there are more than two subsystems in equilibrium in the large isolated system, the transfers of S, V and n. between any pair can be chosen arbitrarily so it follows that at equilibrium all the subsystems must have the same temperature, pressure and chemical potentials. The subsystems can be chosen as very small volume elements, so it is evident that the criterion of internal equilibrium within a system (asserted earlier, but without proof) is unifonnity of temperature, pressure and chemical potentials tlu-oughout. It has now been... 

We have seen that equilibrium in an isolated system (dt/= 0, dF= 0) requires that the entropy Sbe a maximum, i.e. tliat dS di )jjy = 0. Examination of the first equation above shows that this can only be true if. p. vanishes. Exactly the same conclusion applies for equilibrium under the other constraints. Thus, for constant teinperamre and pressure, minimization of the Gibbs free energy requires that dGId Qj, =. p. =... 

The microcanonical ensemble is a set of systems each having the same number of molecules N, the same volume V and the same energy U. In such an ensemble of isolated systems, any allowed quantum state is equally probable. In classical thennodynamics at equilibrium at constant n (or equivalently, N), V, and U, it is the entropy S that is a maximum. For the microcanonical ensemble, the entropy is directly related to the number of allowed quantum states C1(N,V,U) ... 

An explicit example of an equilibrium ensemble is the microcanonical ensemble, which describes closed systems with adiabatic walls. Such systems have constraints of fixed N, V and E < W< E + E. E is very small compared to E, and corresponds to the assumed very weak interaction of the isolated system with the surroundings. E has to be chosen such that it is larger than (Si )... 

For a microcanonical ensemble, p = [F( )] for each of the allowed F( ) microstates. Thns for an isolated system in eqnilibrinm, represented by a microcanonical ensemble. 

The complete thennodynainics of a system can now be obtained as follows. Let die isolated system withAi particles, which occupies a volume V and has an energy E within a small uncertainty E, be modelled by a microscopic Flamiltonian Ti. First, find the density of states p( ) from the Flamiltonian. Next, obtain the entropy as S(E, V, N) = log V E) or, alternatively, by either of the other two equivalent expressions... 

In addition, there could be a mechanical or electromagnetic interaction of a system with an external entity which may do work on an otherwise isolated system. Such a contact with a work source can be represented by the Hamiltonian U p, q, x) where x is the coordinate (for example, the position of a piston in a box containing a gas, or the magnetic moment if an external magnetic field is present, or the electric dipole moment in the presence of an external electric field) describing the interaction between the system and the external work source. Then the force, canonically conjugate to x, which the system exerts on the outside world is... 

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. 

Wlien H has reached its minimum value this is the well known Maxwell-Boltzmaim distribution for a gas in themial equilibrium with a unifomi motion u. So, argues Boltzmaim, solutions of his equation for an isolated system approach an equilibrium state, just as real gases seem to do. Up to a negative factor (-/fg, in fact), differences in H are the same as differences in the themiodynamic entropy between initial and final equilibrium states. Boltzmaim thought that his //-tiieorem gave a foundation of the increase in entropy as a result of the collision integral, whose derivation was based on the Stosszahlansatz. 

The slopes of the fimctions shown provide the reaction rates according to the various definitions under the reaction conditions specified in the figure caption. These slopes are similar, but not identical (nor exactly proportional), in this simple case. In more complex cases, such as oscillatory reactions (chapter A3.14 and chapter C3.6). the simple definition of an overall rate law tluough equation (A3.4.6) loses its usefiilness, whereas equation (A3.4.1) could still be used for an isolated system. 

Rosenstock H M, Wallenstein M B, Wahrhaftig A L and Frying H 1952 Absolute rate theory for isolated systems and the mass spectra of polyatomic molecules Proc. Natl Acad. Sci. USA 38 667-78... 

The mieroeanonieal ensemble eorresponds to an isolated system, with speeified number of partieles N,... 

The second law reqmres that the entropy of an isolated system either increase or, in the limit, where the system has reached an equilibrium state, remain constant. For a closed (but not isolated) system it requires that any entropy decrease in either the system or its surroundings be more than compensated by an entropy increase in the other part or that in the Emit, where the process is reversible, the total entropy of the system plus its surroundings be constant. 

V li = unbalance voltage across the open delta. This is for grounded systems. For isolated systems it will be three times this (Section 15.4.3). 

Nominal voltage Rated current f/J Non-s U gregated phase system Segregated phase system isolated phase system... 

As pointed out in Section 2.4, shock waves are such rapid processes that there is no time for heat to flow into the system from the surroundings they are considered to be adiabatic. By the second law of thermodynamics, the quantity (S — Sg) must be positive for any thermodynamic process in an isolated system. According to (2.54), this quantity can only be positive if the P-V isentrope is concave upward. Thus, the thermodynamic stability condition for a shock wave is... 

Calculation of the energies and forces due to the long-range Coulomb interactions between charged atoms is a major problem in simulations of biological molecules (see Chapter 5). In an isolated system the number of these interactions is proportional to N-, where N is the number of charged atoms, and the evaluation of the electrostatic interactions quickly becomes intractable as the system size is increased. Moreover, when periodic... 

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