Closed system spontaneous processes

Let s look more closely at spontaneous processes and at the thermodynamic driving forces that cause them to occur. We saw in Chapter 8 that most spontaneous chemical reactions are accompanied by the conversion of potential energy to heat. For example, when methane burns in air, the potential energy stored in the chemical bonds of CH4 and 02 is partly converted to heat, which flows from the system (reactants plus products) to the surroundings ... 

For any isolated (closed) system, spontaneous transformations take place with an increase in the entropy AS of the system (see e.g. [2]). For a nonisolated system in isothermal conditions, spontaneous processes take place with a negative variation of free enthalpy AG where ... 

In a process at constant T and V in a closed system doing only expansion work it follows from eq. (1.32) that the spontaneous direction of change is in the direction of decreasing A. At equilibrium the value of A is at a minimum. 

Because processes will be spontaneous in closed systems at constant T and P if they lower the Gibbs free energy (dG/dc < 0), we see that the criterion for a spontaneous reaction in a system at constant T and P is... 

In order to know whether or not a process in a closed system will occur spontaneously, it would be necessary to measure the entropy change in the surroundings (the rest of the universe) and obviously this is not possible. A device is needed to allow deduction of the entropy change of the universe from the process in the closed system. 

The concept of a spontaneous reaction may be a misnomer in general, although a spontaneous process is a more appropriate concept. For (say) a kinetically feasible (closed system) isothermal (Frame 1) gas reaction ... 

The first law of thermodynamics provides a description of the energy balance for a given process the second law provides a criterion for deciding whether or not the process will occur spontaneously. The second law of thermodynamics defines the entropy change (A5, in units of J K l) associated with a change in a closed system in terms of the heat absorbed by the system at constant temperature T ... 

First we must define the term closed system. A system is described as closed if during the process under consideration no transfer of matter either into or out of the system takes place. In other words, the masses of the various components in each phase of the system can vary only as a result of spontaneous physico-chemical reactions occurring within the system. These may be either changes of the physical state of a component, or chemical transformations among the molecules present. 

For a transformation at constant pressure p and temperature T, equilibrium will correspond to a minimum of the free enthalpy. Otherwise, the process would spontaneously continue. For equilibrium, the following expression can be written for the closed system ... 

When AG is negative, the maximum work that can be done by the spontaneous process within a closed system at constant T and P is given by — AG. When AG is positive, the process is not spontaneous, and AG is then the minimum work that must be provided to the system to drive the process. While the reaction pathway followed has no effect on the free energy change of the reaction, the pathway does determine the amount of useful work than can be obtained from a spontaneous reaction process. The free energy change, AG, is a measure of the work that could theoretically be obtained from a reaction, but this amount of work could only be realized if the reaction or process were conducted in a reversible manner, that is, at nearequilibrium conditions where there is a very small driving force. 

At constant temperature and pressure, spontaneous processes occur with a decrease in the free energy, AG, of the closed exchange system. 

This is known as the Clausius inequality and has important applications in irreversible processes. For example, dS > (dQ/T) for an irreversible chemical reaction or material exchange in a closed heterogeneous system, because of the extra disorder created in the system. In summary, when we consider a closed system and its surroundings together, if the process is reversible and if any entropy decrease takes place in either the system or in its surroundings, this decrease in entropy should be compensated by an entropy increase in the other part, and the total entropy change is thus zero. However, if the process is irreversible and thus spontaneous, we should apply Clausius inequality and can state that there is a net increase in total entropy. Total entropy change approaches zero when the process approaches reversibility. 

We take, as the starting point for the identification of an additional thermodynamic variable the experimental obser ation that all spontaneous processes that occur in an isolated constant-volume system result in the evolution of the system to a state of equilibrium (this is a special case of experimental observation 5, Sec. 1.7). The problem is to quantify this qualitative obser ation. We can obtain some insight into how to do this by considering the general balance equation (Eq. 2.1-4) for any extensive variable 9 of a closed, isolated, constant-volume system... 

The development and hatching of a hen s egg after it has been laid presents an interesting situation. Here there is a closed system it is not isolated, since there can be transfer of heat between the egg and its surroundings but no appreciable transfer of material. There is undoubtedly a decrease in entropy as the chicken is formed, since there is an increase in order. Since the process occurs spontaneously it must.be exergonic (AG is negative). In light of the equation... 

It may well be true that the entropy of the universe is increasing (see Chapter 6), but whatever it is doing is quite irrelevant to the study of thermodynamics here on Earth. The difference between the two ways of looking at AS presented above essentially involves two different definitions of the system. In our preferred explanation, the system is the water in the pail, and its entropy decreases spontaneously. In the other view, the system is the universe, by implied hypothesis a closed composite adiabatic system, and the pail a portion of this composite system separated from the rest by diathermal walls. In the overall system, entropy increases. In this view, the choice of system is effectively taken from us—we must choose the universe as our system to preserve the dictum that entropy increases in spontaneous processes. 

This equation is important because it establishes limits on the kinds of processes that can naturally (spontaneously) occur to change the state of a closed system. If two states satisfy the inequality, then the system can spontaneously evolve from the initial to the final state, but only via some irreversible process. If two states fail to satisfy (7.1.12), then the system cannot spontaneously evolve from the initial to the proposed... 

So we have an isolated system divided into two parts each part is initially in its own equilibrium state, as identified by its intensive properties. To initiate a spontaneous process we relax a constraint we remove the partition. Our objective is to test (7.1.18) that is, we want to show that no matter what values are used for the initial temperatures of the gas and alloy, the total entropy never decreases. Note that since one part is a solid, no mass transfer occurs between parts each part is closed. 

A spontaneous adiabatic process in a closed system proceeds in the direction that satisfies the inequality... 

The process of iron being oxidized to make iron(III) oxide (rust) is spontaneous. Which of these statements about this process is/are true (a) The reduction of iron(III) oxide to iron is also spontaneous. (b) Because the process is spontaneous, the oxidation of iron must be fast, (c) The oxidation of iron is endothermic, (d) Equilibrium is achieved in a closed system when the rate of iron oxidation is equal to the rate of iron(III) oxide reduction, (e) The energy of the universe is decreased when iron is oxidized to rust. 

The total Gibbs free energy of a closed system at constant T and P must decrease during a spontaneous irreversible process. During a reversible process, the Gibbs free energy change must be zero ... 

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