Thermodynamics adiabatic processes

See - nonadiabatic (diabatic) process, -> Marcus theory, - Randles, and - Gurney, - adiabatic process (thermodynamics). 

Adiabatic process (thermodynamics) — In - thermodynamics a process is called adiabatic (or isocaloric) if no exchange (gain or loss) of heat occurs between the system and its environment. The word was first used by W.J.M. Rankine in 1859 as a synonym for non-crossing being derived from the classical Greek word adiabatos, meaning something like (it is) forbidden to cross [i]. 

Adiabatic process Thermodynamic change of state of a system in which there is no transfer of heat or mass across the boundaries of the system. 

Adiabatic process Thermodynamic process in which there is no exchange of heat or mass between a metaphorical parcel of air and its surroundings thus, responding to the decrease in atmospheric density with height, rising air cools adiabatically due to expansion and sinking air warms due to compression. 

Adiabatic process. Thermodynamic process without heat exchange be-... 

The first law of thermodynamics has two parts. The first part associates the change in the energy of the system in adiabatic processes to the adiabatic work done on the system ... 

In summaiy, the first law of thermodynamics. Equations la and lb, states that energy is conserved and the energy associated with heat must be included as a form of energy. No process i f is possible if it violates the first law of thermodynamics energy is always conserved in our world as dictated by Equation lb. If Equation lb is applied to an adiabatic process, then because Q = 0 the first part, Equation la is recovered, but one still needs both parts of the first law to define the quantities. 

Thus, in adiabatic processes the entropy of a system must always increase or remain constant. In words, the second law of thermodynamics states that the entropy of a system that undergoes an adiabatic process can never decrease. Notice that for the system plus the surroundings, that is, the universe, all processes are adiabatic since there are no surroundings, hence in the universe the entropy can never decrease. Thus, the first law deals with the conservation of energy in any type of process, while the sec-... 

After identifying the initial temperature (T) and pressure (P) values, the final temperature and both enthalpy values (H) can be read on the same entropy line of the appropriate gas Mollier chart. For the adiabatic process, the work done on the gas is equal to AH, see Figures 12-13A-D. The following is reproduced by permission of Edmister, W. C., Applied Hydrocarbon Thermodynamics, Gulf Publishing Company. ... 

The second law of thermodynamics states that energy exists at various levels and is available for use only if it can move from a higher to a lower level. For example, it is impossible for any device to operate in a cycle and produce work while exchanging heat only with bodies at a single fixed temperature. In thermodynamics, a measure of the unavailability of energy has been devised and is known as entropy. As a measure of unavailability, entropy increases as a system loses heat, but remains constant when there is no gain or loss of heat as in an adiabatic process. It is defined by the following differential equation ... 

We have seen how to calculate q for the isochoric and isobaric processes. We indicated in Chapter 1 that q = 0 for an adiabatic process (by definition). For an isothermal process, the calculation of q requires the application of other thermodynamic equations. For example, q can be obtained from equation (2.3) if AC and w can be calculated. The result is... 

As we have seen before, exact differentials correspond to the total differential of a state function, while inexact differentials are associated with quantities that are not state functions, but are path-dependent. Caratheodory proved a purely mathematical theorem, with no reference to physical systems, that establishes the condition for the existence of an integrating denominator for differential expressions of the form of equation (2.44). Called the Caratheodory theorem, it asserts that an integrating denominator exists for Pfaffian differentials, Sq, when there exist final states specified by ( V, ... x )j that are inaccessible from some initial state (.vj,.... v )in by a path for which Sq = 0. Such paths are called solution curves of the differential expression The connection from the purely mathematical realm to thermodynamic systems is established by recognizing that we can express the differential expressions for heat transfer during a reversible thermodynamic process, 6qrey as Pfaffian differentials of the form given by equation (2.44). Then, solution curves (for which Sqrev = 0) correspond to reversible adiabatic processes in which no heat is absorbed or released. 

In the neighborhood of every equilibrium state of a thermodynamic system, there exist states unattainable from it by any adiabatic process (reversible or irreversible). 

Like the engine-based statements, Caratheodory s statement invokes limitations. From a given thermodynamic state of the system, there are states that cannot be reached from the initial state by way of any adiabatic process. We will show that this statement is consistent with the Kelvin-Planck statement of the Second Law. 

Since q >0, and l/T > /T2 with T2 >7), we conclude that AS for this allowed, spontaneous process is greater than zero. Having obtained this result for the specific case, we can extend it to the general case, because our earlier conclusion that there is an allowed direction to spontaneous adiabatic processes applies to all thermodynamic systems. 

KEY TERMS First Law of Thermodynamics adiabatic process heat work internal energy... 

For elementary adiabatic process CvdT = —5A, where Cv is the heat of the w-ball, 8A is the elementary work in the systems of the thermodynamics signs. Due to determination of the conformation pressure we can write SA = PdV and, thereby... 

The first law of thermodynamics applied to an adiabatic system may be expressed as the work done on a system by an adiabatic process, which is equal to the increase in its internal energy, and a function of the state of the system. 

Second Law of Thermodynamics. There have been numerous statements of the second law. To paraphrase Clausius It is impossible to devise an engine or process which, working in a cycle, will produce no effect other than the transfer of heat from a colder to a warmer body. According to Caratheodory, the Second Law can be stated as follows Arbitrarily close to any given state of any closed system, there exists an unlimited number of other states which it is impossible to reach from a given state as a result of any adiabatic process, whether reversible or not . 

Compression of hydrogen consumes energy depending on the thermodynamic process. The ideal isothermal compression requires the least amount of energy (just compression work) and the adiabatic process requires the maximum amount of energy. The compression energy W depends on the initial pressure p and the final pressure pf, the initial volume V and the adiabatic coefficient y ... 

The terms adiabatic and nonadiabatic are confusing. Thus, students who approach kinetics at an electrochemical interface via studies of chemistiy will be used to the term adiabatic. In thermodynamics, adiabatic indicates a process in which no heat enters or escapes from the system, e.g., from the vessel in which the reaction... 

ADIABATIC PROCESS. Any thermodynamic process, reversible or irreversible, which takes place in a system without the exchange of heat with the surroundings. When the process is also reversible, it is called isentropic, because, then the entropy of the system remains constant at every step of the process, fin older usage, isentropic processes were called simply adiabatic, or quasistatic adiabatic the distinction between adiabatic and isentropic processes was not always sharply drawn.)... 

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. 

Adiabatic Process.—This term is often seen in spectroscopic and photochemical literature and used in a different sense than its usual thermodynamic meaning. In Herzberg s opinion (15) adiabatic processes should be defined as reactions or processes in which no change of electronic state occurs and in which the velocity of the partners is sufficiently small that at every point the electronic energy takes on the value corresponding to the particular values of the coordinates. A non-adiabatic process is one in which there is a change in electronic state. ... 

The inequalities of the previous paragraph are extremely important, but they are of little direct use to experimenters because there is no convenient way to hold U and S constant except in isolated systems and adiabatic processes. In both of these inequalities, the independent variables (the properties that are held constant) are all extensive variables. There is just one way to define thermodynamic properties that provide criteria of spontaneous change and equilibrium when intensive variables are held constant, and that is by the use of Legendre transforms. That can be illustrated here with equation 2.2-1, but a more complete discussion of Legendre transforms is given in Section 2.5. Since laboratory experiments are usually carried out at constant pressure, rather than constant volume, a new thermodynamic potential, the enthalpy H, can be defined by... 

For an adiabatic process the equilibrium and frozen composition expansion processes are both isentropic, whereas the finite rate process is not. The following thermodynamic development following (24) explicitly verifies this statement. 

Other specifications for the product, such as pressure and heat duty (e.g., adiabatic processes) or pressure and entropy (e.g., isentropic processes) also involve finding the extremum of a thermodynamic function. Given pressure and heat duty, the entropy is maximized... 

The fallacy of this view arises in conjunction with a concept of adiabatic processes. Adiabatic enclosures are ideal partitions which separate regions of thermodynamic interest from the remainder of the universe in particular, no heat transfer of any type can occur across those boundaries. In the present example, however, the walls of the container are in intimate contact with the gas which is being compressed. Thus, these walls cannot be considered as part of the adiabatic partition which separates the container plus contents from the remainder of the universe. 

We have also pointed out here the formal connection between our formalism and the existing numerical algorithms in special cases (CP-algorithm and time-dependent optimized potential) as well as avenues to go beyond these to include non-adiabatic processes. It should be stressed that unlike the existing theories, our framework is based on a stationary action principle, which facilitates incorporation of the initial constraint of thermodynamic equilibrium. This development is made feasible by working in a superspace formalism. This work thus provides a practical theoretical framework for studying the non-equilibrium statistical mechanics of systems initially in thermodynamic equilibrium. 

A thermodynamic quantity of considerable importance in many combustion problems is the adiabatic flame temperature. If a given combustible mixture (a closed system) at a specified initial T and p is allowed to approach chemical equilibrium by means of an isobaric, adiabatic process, then the final temperature attained by the system is the adiabatic flame temperature T. Clearly depends on the pressure, the initial temperature and the initial composition of the system. The equations governing the process are p = constant (isobaric), H = constant (adiabatic, isobaric) and the atom-conservation equations combining these with the chemical-equilibrium equations (at p, T ) determines all final conditions (and therefore, in particular, Tj). Detailed procedures for solving the governing equations to obtain Tj> are described in [17], [19], [27], and [30], for example. Essentially, a value of Tf is assumed, the atom-conservation equations and equilibrium equations are solved as indicated at the end of Section A.3, the final enthalpy is computed and compared with the initial enthalpy, and the entire process is repeated for other values of until the initial and final enthalpies agree. 

Define the terras closed process system, open process system, isothermal process, and adiabatic process. Write the first law of thermodynamics (the energy balance equation) for a closed process system and state the conditions under which each of the five terms in the balance can be neglected. Given a description of a closed process system, simplify the energy balance and solve it for whichever term is not specified in the process description. 

Dhar modelled the stretching of a polymer using the stochastic Rouse model, for which distributions of various definitions of the work can be obtained. Two mechanisms for the stretching were considered one where the force on the end of the polymer was constrained and the other where its end was constrained. Dhar commented that the variable selected for the work was only clearly identified as the entropy production in the latter case. In the former case they argue that the average work is non-zero for an adiabatic process, and therefore should not be considered as an entropy production, however we note that the expression is consistent with a product of flux and field as used in linear irreversible thermodynamics. 

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