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Thermodynamic Equilibrium

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A system in in thermodynamic equilibrium when its pressure, temperature and composition are same throughout its size (generally volume). This operational definition requires almost an infinite number of measurements that is at all points in the system. Consequently it is convenient to define thermodynamic equilibrium in the following form comprising three criteria mechanical equilibrium, thermal equilibrium and chemical equilibrium.

The advantage of thermodynamic equilibrium is that the function which defines its behavior is simple. In the case of non-equilibrium, pressure, temperature and composition are not defined for a system as a whole.

Definition

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Definition

"Thermodynamic equilibrium is a situation in which the distributions of all thermodynamic observables have caused to change with time."

For certain systems this may take a very long time indeed for example for a piece of glass it may take thousands of years for thermodynamic equilibrium to be reached.

Conditions

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The thermodynamic processes are rarely studied under conditions of constant entropy or constant energy, it is desirable to obtain criteria for thermodynamic equilibrium under practical conditions such as constant pressure.

Under condition of constant h and p, the equilibrium is reached for dh = 0. Under conditions of constant T and p, equilibrium is specified for the condition dg = 0. The thermodynamic equilibrium conditions are thus summarized as
  • At constant $\eta$, $\nu$: du = 0, d2u>0
  • At constant $\eta$, p: dh = 0, d2h>0
  • At constant T, $\nu$: da = 0, d2a>0
  • At constant T, p: dg = 0, d2g>0

Stability

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Thermodynamic stability involves the position of a particular equilibrium and so it is set by $\Delta$Go.

At one bar pressure and the given temperature
  1. If $\Delta G_{f}^{{\circ}}$ > 0, the compound is thermodynamically unstable with respect to its elements.
  2. If $\Delta G_{f}^{{\circ}}$ < 0, the compound tends to form spontaneously from its elements and is said to be thermodynamically stable with respect to its elements.

Equilibrium Constant

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The thermodynamic equilibrium constant K is the equilibrium constant in which the concentration of gases are expressed in partial pressures in atmospheres, whereas the concentration of solutes in liquid solutions is expressed in molarities.

For the following generalized equation, the thermodynamic equilibrium constant is defined in terms of the activities of the species involved.

aA + bB $\rightleftharpoons$ cC + dD

$K=\frac{(a_{C}^{c})(a_{D}^{d})}{(a_{A}^{a})(a_{B}^{b})}$

Where aA is the activity of substance A and so on.