Adiabatic process isolated system

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. ... 

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... 

E3.7 A block of copper weighing 50 g is placed in 100 g of HiO for a short time. The copper is then removed from the liquid, with no adhering drops of water, and separated from it adiabatically. Temperature equilibrium is then established in both the copper and water. The entire process is carried out adiabatically at constant pressure. The initial temperature of the copper was 373 K and that of the water was 298 K. The final temperature of the copper block was 323 K. Consider the water and the block of copper as an isolated system and assume that the only transfer of heat was between the copper and the water. The specific heat of copper at constant pressure is 0.389 JK. g l and that of water is 4.18 J-K 1-g 1. Calculate the entropy change in the isolated system. 

For an isolated (adiabatic) system, AS > 0 for any natural (spontaneous) process from State a to State b, as was proved in Section 6.8. An alternative and probably simpler proof of this proposition can be obtained if we use a temperature-entropy diagram (Fig. 6.13) instead of Figure 6.8. In Figure 6.13, a reversible adiabatic process is represented as a vertical line because AS = 0 for this process. In terms of Figure 6.13, we can state our proposition as follows For an isolated system, a spontaneous process from a to b must lie to the right of the reversible one, because AS = Sb Sa> 0. 

Consider any number of systems that may do work on each other and also transfer heat from one to another by reversible processes. The changes of state may be of any nature, and any type of work may be involved. This collection of systems is isolated from the surroundings by a rigid, adiabatic envelope. We assume first that the temperatures of all the systems between which heat is transferred are the same, because of the requirements for the reversible transfer of heat. For any infinitesimal change that takes place within the isolated system, the change in the value of the entropy function for the ith system is dQJT, where Qt is the heat absorbed by the ith system. The total entropy change is the sum of such quantities over all of the subsystems in the isolated system, so... 

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... 

Therefore, the total entropy produced within the system must be discharged across the boundary at stationary state. For a system at stationary state, boundary conditions do not change with time. Consequently, a nonequilibrium stationary state is not possible for an isolated system for which deS/dt = 0. Also, a steady state cannot be maintained in an adiabatic system in which irreversible processes are occurring, since the entropy produced cannot be discharged, as an adiabatic system cannot exchange heat with its surroundings. In equilibrium, all the terms in Eq. (3.48) vanish because of the absence of both entropy flow across the system boundaries and entropy production due to irreversible processes, and we have dJS/dt = d dt = dS/dt = 0. 

One additional feature of the Second Law must be taken up at this point, which relates to the entropy change incurred in a finite, possibly irreversible process in an adiabatically isolated system. Consider such a system in an initial state characterized by the set of deformation variables xx and entropy Si and its transition to a final state 2 associated with x2... 

Herein, then, one can detect a very important useful property of the entropy function It provides an indication whether or not a contemplated process can proceed spontaneously in an adiabatically or totally isolated system. For such a process to occur it is necessary that the entropy of the final state of the system be greater than that of the initial state. If the reverse situation holds, the process under study operates in the opposite sense. 

Let us simplify the notation by setting dQj" 2 = dX and dQj 2 - IdS1" 2 TdS. One must now consider the possibilities (a) dQi - TdS > 0, i.e., TdS < dQi, or (b) dQi - TdS < 0, i.e., TdS > dQA. The present discussion must apply to all cases including the special situation where the irreversible process is carried out adiabatically. Under alternative (b) one then obtains TdS > 0 for the adiabatically isolated system, and no contradictions are uncovered. Under alternative (a) one would require TdS < 0 for an irreversible, adiabatic process, and by the corollary to the Second Law, discussed in Section 1.13, this possibility must be ruled out. We thus claim that... 

We emphasize once more that the state function S serves as a means of monitoring whether a given process in an adiabatically isolated system is indeed possible. No process for which S decreases can occur in an adiabatically isolated system conversely, any process for which S increases in such a system will be spontaneous. 

So far in this chapter we have focused on isothermal (constant-temperature) processes for ideal gases. In this section we introduce the adiabatic process— a process in which no energy as heat flows into or out of the system. That is, an adiabatic process occurs when the system is thermally isolated (insulated) from the surroundings. For an adiabatic process... 

An adiabatic enclosure is filled with supercooled water and then allowed to stand in due time ice is observed to form. Obviously, the process is spontaneous, yet there is a decrease in overall order, hence, a reduction in entropy. How can this be reconciled with the statement that the entropy of an isolated system can only increase ... 

We now examine several equilibration processes in detail. The first relates to thermal conditions which prevail when two adjacent isolated systems, designated as and ", initially at temperature T and T", are equilibrated, after allowing their rigid adiabatic partition to become slightly diathermic (see Fig. 2.2.1). The restriction that the compound system remain isolated and that the energies and entropies be additive yields the relations (ignoring interfacial contributions)... 

A thermally isolated system is a special case of the closed system, where no transfer of mass or heat can take place but the performance of work is allowed. A process taking place in a thermally isolated system is referred to as an adiabatic 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. 

We consider an arbitrary adiabatically isolated system consisting of two parts in thermal contact. The system is at a uniform temperature t, and we assume that the equilibrium states of each of the parts can be characterized by t and one other parameter. Thus, for a quasi-static process,... 

According to the second law of thermodynamics, diS = 0 for the equilibrium processes, and for non-equilibriiun processes ifS > 0. For an adiabatic isolated system, that is for a system, which can not exchange its heat or substance with the enviromnent, d S = 0, and it follows from (5.119)... 

This shows that thermodynamic constraints on isolated systems are the same as those for adiabatic processes on closed systems. 

The concept of a potential energy surface, arising from the adiabatic approximation, is the basis of both the classical and quantum-mechanical treatment of the dynamics of elastic, inelastic and reactive collisions. The adiabatic potential energy V(x) governs the internal motions of atoms in an isolated system and determines the solutions of the nuclear wave equation (6.1) However, the results of a collision process will be entirely determined by the interaction potential V(x) only if the translation and rotation motion of the overall system do not influence its internal motions ... 

To fix ideas, consider the following experiment an insulated cylinder is divided by a movable wall into two compartments, one that contains a hot pressurized gas, and one that contains a colder, low-pressure gas (state A). The separating wall, which is conducting, is held into place with latches. The latches are removed and the system is left undisturbed to reach its final equilibrium state (state B), which, experience teaches, is a state of uniform pressure and temperature across both compartments. This process is spontaneous and adiabatic. Our development is motivated by the tendency of isolated systems like this to reach equilibrium. This tendency defines a preferred direction towards the equilibrium state, never away from it. We recognize that such directionality cannot be represented by an equality it requires an inequality so that if it is satisfied in one direction it is violated in the opposite one. At equilibrium, this inequality must reduce to an exact equality, so that the direction of change is neither forward nor backward—without this special condition, a system would never reach equilibrium. Moreover, the quantity in the inequality that fixes this direction must be such that if its change is positive in one direction, it will be negative in the opposite direction, so that the process may proceed in one direction only. It must, therefore, be a state function. Finally, since the state of a nonequilibrium system is nonuniform but consists of various parts in their own local states, the property we are after must be extensive, so that all parts of the system... 

Before introducing the notion of nonequilibrium thermodynamics we shall first summarize briefly the linear and nonlinear laws between thermodynamic fluxes and forces. A key concept when describing an irreversible process is the macroscopic state parameter of an adiabatically isolated system These parameters are denoted by. At equilibrium the state parameters have values A , while an arbitrary state which is near or far from the equilibrium may be specified by the deviations from the equilibrium state ... 

If the system is thermally isolated to prevent energy flow in the form of heat (but possibly allowing for work to be done on the system), then any process occurring within this system will have q = 0. Any process with = 0 is called an adiabatic process. 

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