Stress equilibrium, principle

We can actually go one step further than this general observation and use the stress equilibrium principle applied to the tetrahedron to obtain a simple expression for the surface-stress vector t on an arbitrarily oriented surface at x in terms of the components of t on the three mutually perpendicular surfaces at the point x. We denote the stress vector on a surface with normal n as t(n). The area of the surface with unit normal n is denoted as A A . Then, applying the surface-stress equilibrium principle to the tetrahedron, we have... 

This result is sometimes called the principle of stress equilibrium, because it shows that the surface forces must be in local equilibrium for any arbitrarily small volume element centered at any point x in the fluid. This is true independent of the source or detailed form of the surface forces. 

The minus sign in this equation is a matter of convention t(n) is considered positive when it acts inward on a surface whereas n is the outwardly directed normal, andp is taken as always positive. The fact that the magnitude of the pressure (or surface force) is independent of n is self-evident from its molecular origin but also can be proven on purely continuum mechanical grounds, because otherwise the principle of stress equilibrium, (2 25), cannot be satisfied for an arbitrary material volume element in the fluid. The form for the stress tensor T in a stationary fluid follows immediately from (2 59) and the general relationship (2-29) between the stress vector and the stress tensor ... 

A buffer solution functions in accordance with LeChatelier s principle, which states that an equilibrium system, when stressed, will shift its equilibrium to relieve that stress. This principle is illustrated by the following examples. 

If the four components are in a state of equilibrium, as determined by the equilibrium constant, addition or removal of one of the components would cause the equilibrium to reestablish itself. For example, suppose we add more iron(II) to the solution. According to Le Chatelier s principle, the reaction will shift to the left to relieve the stress. Equilibrium will eventually be reestablished, and its position will still be defined by the same equilibrium constant. 

In plane truss analysis condition, the stress state generated by comprehensive effects of adding tie rod is same to that of finite element analysis. So according to the mechanical equilibrium principle, the following equation is established. 

In 1888, the French chemist Henri Louis Le ChStelier developed a principle that provides a means of predicting the influence of stress factors on equihbrium systems. Le Chateher s principle states that if a system at equilibrium is subjected to a stress, the equilibrium is shifted in the direction that tends to relieve the stress. This principle is true for all dynamic equilibria, chemical as well as physical. Changes in pressure, concentration, and temperature illustrate Le Chcktelier s principle. 

A solid, by definition, is a portion of matter that is rigid and resists stress. Although the surface of a solid must, in principle, be characterized by surface free energy, it is evident that the usual methods of capillarity are not very useful since they depend on measurements of equilibrium surface properties given by Laplace s equation (Eq. II-7). Since a solid deforms in an elastic manner, its shape will be determined more by its past history than by surface tension forces. 

According to Le Chatelier s principle, a system at equilibrium adjusts so as to mini mize any stress applied to it When the concentration of water is increased the system responds by consuming water This means that proportionally more alkene is converted to alcohol the position of equilibrium shifts to the right Thus when we wish to pre pare an alcohol from an alkene we employ a reaction medium m which the molar con centration of water is high—dilute sulfuric acid for example... 

The observation that a system at equilibrium responds to a stress by reequilibrating in a manner that diminishes the stress, is formalized as Le Chatelier s principle. One of the most common stresses that we can apply to a reaction at equilibrium is to change the concentration of a reactant or product. We already have seen, in the case of sodium acetate and acetic acid, that adding a product to a reaction mixture at equilibrium converts a portion of the products to reactants. In this instance, we disturb the equilibrium by adding a product, and the stress is diminished by partially reacting the excess product. Adding acetic acid has the opposite effect, partially converting the excess acetic acid to acetate. 

Le Chatelier s principle provides a means for predicting how systems at equilibrium respond to a change in conditions. When a stress is applied to an equilibrium by adding a reactant or product, by adding a reagent that reacts with one of the reactants or products, or by changing the volume, the system responds by moving in the direction that relieves the stress. 

Le Chatelier s principle when stressed, a system that was at equilibrium returns to its equilibrium state by reacting in a manner that relieves the stress, (p. 148)... 

Le Chatelier s principle (Section 6.10) A reaction at equilibrium responds to any stress imposed on it by shifting the equilibrium in the direction that minimizes the stress. 

Le Chatelier s principle When a stress is applied to a system in dynamic equilibrium, the equilibrium tends to adjust to minimize the effect of the stress. 

Le Chatelier s principle When a stress is applied to a system in dynamic equilibrium, the equilibrium adjusts to minimize the effect of the stress. Example a reaction at equilibrium tends to proceed in the endothermic direction when the temperature is raised, leveling The observation that strong acids all have the same strength in water, and all behave as though they were solutions of H,Of ions. 

Chemical equilibria being of a dynamic type, equilibrium states are altered by changes in the variables controlling them. The effect of such changes can be interpreted qualitatively on the basis of a principle which was enunciated independently by Le Chatelier in 1885 and by Braun one year later. It states that when a system in a state of dynamic equilibrium is subjected to a stress imposed by variation in anyone of the variables controlling the equilibrium state, the system will tend to adjust itself in such a way as to minimize the effect of the stress. The variables of interest in this connection are temperature of the system, pressure on the system, and concentrations for the reactants and products taken individually. 

Failure to remove the alcohols generated in either of the equilibrium condensation steps will reduce the efficiency of the polymerization process. This effect can be explained by Le Chatelier s principle, which was discussed in Chapter 3. The volatile alcohols produced during polymerization act as a chemical stress on the product side of the reaction, which inhibits polymerization. Another implication of the equilibrium nature of this polymerization process is seen in the molecular weight distribution of the final polymer. All polyesters contain a few percent of low molecular weight oligomers, regardless of the polymerization process. 

Le Chatelier s principle states that if a stress is applied to a system at equilibrium, the equilibrium will shift in a tendency to reduce that stress. A stress is something done to the system (not by the equilibrium reaction). The stresses that we consider are change of temperature, change of pressure, change of concentration(s), and addition of a catalyst. Let us consider the effect on a typical equilibrium by each of these stresses. 

Pressure affects the gases in a system much more than it affects the liquid or solids. We will investigate the same ammonia, hydrogen, nitrogen system discussed above. If the system is at equilibrium, what will an increase in pressure by the chemist do to the equilibrium The system will shift to try to reduce the stress, as required by Le Chatelier s principle. How can this system reduce its own pressure By reducing the total number of moles present. It can shift to the right to produce 2 mol of gas for every 4 mol used up ... 

Identify or explain each of the following terms (a) equilibrium. (b) rate of reaction, (c) catalyst. (d) completion, (e) Le Chatclicr s principle, (/) stress, (g) shift, (/ ) shift to the right or left, (i) equilibrium constant, and (j) equilibrium constant expression. 

At a given temperature, a reaction will reach equilibrium with the production of a certain amount of product. If the equilibrium constant is small, that means that not much product will be formed. But is there anything that can be done to produce more Yes, there is— through the application of Le Chatelier s principle. Le Chatelier, a French scientist, discovered that if a chemical system at equilibrium is stressed (disturbed) it will reestablish equilibrium by shifting the reactions involved. This means that the amounts of the reactants and products will change, but the final ratio will remain the same. The equilibrium may be stressed in a number of ways changes in concentration, pressure, and temperature. Many times the use of a catalyst is mentioned. However, a catalyst will have no effect on the equilibrium amounts, because it affects both the forward and reverse reactions equally. It will, however, cause the reaction to reach equilibrium faster. 

Le Chatelier s principle says that if an equilibrium system is stressed, it will reestablish equilibrium by shifting the reactions involved. A change in concentration of a species will cause the equilibrium to shift to reverse that change. A change in pressure or temperature will cause the equilibrium to shift to reverse that change. 

Le Chatelier s principle Le ChOtelier s principle states that if a chemical system at equilibrium is stressed (disturbed), it will reestablish equilibrium by shifting of the reactions involved, limiting reactant The limiting reactant is the reactant that is used up first in a chemical reaction, line spectrum A line spectrum is a series of fine lines of colors representing wavelengths of photons that are characteristic of a particular element, liquid A liquid is a state of matter that has a definite volume but no definite shape, macromolecules Macromolecules are extremely large molecules. 

Le Chatelier s principle is a powerful tool for explaining how a reaction at equilibrium shifts when a stress is placed on the system. In this experiment, you can use Le Chatelier s principle to evaluate the relative solubilities of two precipitates. By observing the formation of two precipitates in the same system, you can infer the relationship between the solubilities of the two ionic compounds and the numerical values of their solubility product constants (K ). You will be able to verify your own experimental results by calculating the molar solubilities of the two compounds using the Ksp for each compound. 

The first ingredient in any theory for the rheology of a complex fluid is the expression for the stress in terms of the microscopic structure variables. We derive an expression for the stress-tensor here from the principle of virtual work. In the case of flexible polymers the total stress arises to a good approximation from the entropy of the chain paths. At equilibrium the polymer paths are random walks - of maximal entropy. A deformation induces preferred orientation of the steps of the walks, which are therefore no longer random - the entropy has decreased and the free energy density/increased. So... 

Another crystallization technique is used when the isolation of a highly water-soluble compound in its salt form is required from aqueous reaction mixtures. This technique takes advantage of the common-ion effect and is based on the le Chatelier s principle, which states that, if, to a system in equilibrium, a stress is applied, the system will react so as to relieve the stress. Thus, in aqueous solutions, the solubility of the compound in salt form can be reduced by adding large amoimts of a common ion which is more soluble than the salt of the compoimd. 

Given LeChatelier s Principle (when a stress is placed on a system at equilibrium, the system will adjust itself in such a way as to relieve the stress), it seemed that if... 

The final stress to be considered is a change in temperature. To apply Le Chate-lier s Principle with temperature changes, the sign of AH for the reaction needs to be known. The AH in our example is = +131 kilojoules. This indicates that the forward reaction is endothermic and the reverse reaction is exothermic. When the temperature of a system at equilibrium is increased, the equilibrium will favor the endothermic reaction. One way to think of the effect of temperature is to think of energy as a reactant or product. This is seen when the forward and reverse reactions are written as two separate reactions ... 

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