stable equilibrium

Examples of stable equilibrium in the following topics:

• Thermal Instability

  • If the power absorbed and generated within the gas equals the power emitted by the gas, the temperature of the gas will remain constant and equilibrium is achieved.
  • The question remains whether this equilibrium is stable.
  • Heuristically we can see that if the cooling rate increases faster with temperature than the heating rate, then a slight increase in temperature will result in the gas cooling faster and the temperature returning to its equilibrium value.

• Stereogenic Nitrogen

  • If these configurations were stable, there would be four additional stereoisomers of ephedrine and pseudoephedrine.
  • However, pyramidal nitrogen is normally not configurationally stable.
  • It rapidly inverts its configuration (equilibrium arrows) by passing through a planar, sp2-hybridized transition state, leading to a mixture of interconverting R and S configurations.
  • If the nitrogen atom were the only chiral center in the molecule, a 50:50 (racemic) mixture of R and S configurations would exist at equilibrium.

• Stability, Balance, and Center of Mass

  • An object in static equilibrium remains in the same state forever, but not all forms of equilibrium are the same.
  • When the first derivative is zero, we can take the second derivative to find whether the equilibrium is stable or unstable.
  • \frac{d^2 U(x)} {dx^2} \right|_{x_0} > 0$, then the system is stable; conversely, if the potential is concave-down, then the equilibrium is unstable.
  • If the second derivative is zero or does not exist, then the equilibrium is neutral—neither stable nor unstable.
  • This is an example of unstable equilibrium.

• Period of a Mass on a Spring

  • Once released, the restoring force causes the ruler to move back toward its stable equilibrium position, where the net force on it is zero.
  • The maximum displacement from equilibrium is known as the amplitude X .
  • The object's maximum speed occurs as it passes through equilibrium.
  • (d) The equilibrium point is reach again, this time with momentum to the right.
  • It stops the ruler and moves it back toward equilibrium again.

• Ecological Succession

  • Communities with a stable structure are said to be at equilibrium.
  • Following a disturbance, the community may or may not return to the equilibrium state.
  • Over time, the area will reach an equilibrium state with a set of organisms quite different from the pioneer species.
  • Eventually, over 150 years, the forest will reach its equilibrium point where species composition is no longer changing and resembles the community before the fire.
  • This equilibrium state is referred to as the climax community, which will remain stable until the next disturbance.

• Market Adjustment to Change

  • A decrease in demand will cause both the equilibrium price and quantity to fall.
  • An increase in supply (while demand is constant) will cause the equilibrium price to decrease and the equilibrium quantity to increase.
  • A decrease in supply will result in an increase is the equilibrium price and a decrease in equilibrium quantity.
  • However, the decrease in demand reduces the equilibrium quantity while the increase in supply pushes the equilibrium quantity up.
  • Whether equilibrium is a stable condition from which there "is no endogenous tendency to change," or and outcome which the economic process is tending toward," equilibrium represents a coordination of objectives among buyers and sellers.

• Finding an Equilibrium Exchange Rate

  • There are two methods to find the equilibrium exchange rate between currencies; the balance of payment method and the asset market model.
  • The concept of purchasing power parity is important for understanding the two models of equilibrium exchange rates below.
  • The balance of payments model holds that foreign exchange rates are at an equilibrium level if they produce a stable current account balance.
  • After an intermediate period, imports will be forced down and exports will rise, thus stabilizing the trade balance and bringing the currency towards equilibrium.
  • The asset market model views currencies as an important element in finding the equilibrium exchange rate.

• Market-Oriented Theories

  • When the supply of a product exactly meets the demand for it, the price reaches a state of equilibrium and no longer fluctuates.
  • Considering inequality, market-oriented theories claim that if left to the free-market, all products and services will reach equilibrium, and price stability will reduce inequality.
  • With less supply and stable demand, the wage for agricultural labor will rise to a sustainable level.
  • Generally, market-oriented theories hold that when supply of labor and goods meets demand, the economic order will reach equilibrium, and inequality will either be non-existent or will be stable.

• Chromium

  • Chromium exhibits a wide range of possible oxidation states, where the +3 state is the most stable energetically.
  • Most important are the chromate (CrO42-) and dichromate (Cr2O72-) anions, which exist in equilibrium:
  • The change in equilibrium is visible by a change from yellow (chromate) to orange (dichromate), such as when an acid is added to a neutral solution of potassium chromate.
  • Many chromium(II) compounds are known, including the water-stable chromium(II) chloride (CrCl2).
  • The resulting bright blue solution is only stable at neutral pH.

• Introduction to Monetary Policy

  • Monetary policy is the process by which a monetary authority controls the money supply, often to produce stable prices and low unemployment.
  • The official goals usually include relatively stable prices and low unemployment.
  • Without a policy intervention the output gap may correct itself, if falling wages and prices shift the short-run aggregate supply curve to the right until the economy returns to the long-run equilibrium.
  • Suppose, for example, that high short-run aggregate demand creates an equilibrium in which prices are higher than in the long-run equilibrium.