[Physics] Question on entropy

entropystatistical mechanicsthermodynamics

All of my textbooks mention, that entropy-change of all spontaneous physical, and chemical processes is positive, and that such processes need another condition to fulfill- decrease in the net internal-energy of the system, taking part in the process.

I just want to know that what is the reason behind this tendency of a system to increase its entropy, and to lose its internal-energy.

Best Answer

Perhaps my ensuing answer will be a little too simple to be satisfying to you, but I only have a firm grasp of things when I keep it simple.

Let's just consider statistical mechanics and look at the Canonical Ensemble (where there's a constant number of particles [N], volume [V], and temperature [T]). The components that make up this system want to reach equilibrium because that's how thermodynamic systems behave. The equilibrium point in the Canonical Ensemble is defined as the point at which the Helmholtz Free Energy, A, is minimized, and it's defined as: A = U - TS where U is potential energy (a negative value) and S is entropy. Entropy is also defined in stat mech as S = -k ln(W) where k is the Boltzmann constant and W is the number of microstates in a system.

What does this mean? A system in equilibrium doesn't always increase its entropy, rather it minimizes its free energy and one way to minimize free energy is to maximize entropy. Let's consider the three different states of H2O: at low temperatures, hydrogen bonds (i.e. potential energy) dominate free energy and the system exists as a low entropy solid. At intermediate temperatures, neither potential energy or entropy dominate and its a liquid. At high temperatures, the entropy term dominates and the water molecules exist far away from each other so as to have an extremely high number of microstates, and very little potential energy.