Part I : Preliminaries (Thermodynamics and Kinetics)
Module 1: Gibbs free energy and equilibria
 

Consider the Gibbs free energy (\begin{displaymath} G = U + P V - T S = H - T S \end{displaymath}) defined as follows:

$U$ (1)
where $P$is the internal energy, $V$ is the pressure, $T$is the volume, $S$ is the temperature, $H$ is the entropy and is the enthalpy [1]. In a material which is at a constant temperature and pressure, if we plot the Gibbs free energy as a function of different internal configurations, then, much like the Tanjore doll, the system chooses that configuration for which the Gibbs free energy is minimum.

Now, let us consider a slightly more complicated mechanical system than the Tanjore doll: See Fig. 2. If the block is kept horizontally, the gravitational potential energy (gravitational energy) is the minimum. Any disturbance from this position takes the block back to horizontal position. However, there is another relatively stable position, namely vertical as shown. In this case also, any slight disturbances take the block back to the vertical position. However, if we stand the block on one edge as shown, any small perturbation will make the block reach the vertical or horizontal position. This configuration is known as equilibrium configurations for the block. The vertical position is known as the metastable equilibirum because even though the block prefers this position for small disturbances, larger disturbances pushes it to a different position. The horizontal position is known as the stable equilibrium because this is the minimum energy position and there are no other positions for which the gravitational potential energy is less than that for this position. Finally, a block standing on its edge is known as unstable equilibrium. to the right and left, it comes back to the original position. This is because, as shown in the Figure1, the potential energy increases for small deviations from the given position. Such a state is known as metastable state. However, if the block is pushed to the peak point as shown, any small perturbation will make it fall down. Such a state is known as unstable state . Finally, when the block reaches the third position as shown(or made to stand at the corner). It is not stable at all. The potential energy is maximum for this configuration. Such a configuration is known as unstable configuration.