Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This degree of randomness or disorder is quantified using a physical quantity known as entropy, denoted by the symbol 'S.'

For an isothermal reversible process, the change in entropy is calculated from the ratio of the heat exchanged to the temperature at which the process occurs. For each infinitesimally small change in entropy, 'dS' equals the infinitesimally small change in energy ‘dq’ flowing into the system divided by the temperature at that specific time.

If we consider a system taken reversibly from state A to B where the temperature isn't constant, then the change in entropy for all infinitesimal processes at different temperatures is calculated by integrating the energy supplied as heat at each stage of the path over the temperature at which that heat is transferred. Entropy, being an extensive property, has units of joules per kelvin (J/K).

Moreover, the total entropy change in any isolated system is always positive, leading to an alternative formulation of the second law of thermodynamics: the total entropy of a system during any spontaneous process either increases or remains constant; it never decreases. This principle implies that heat spontaneously transfers from hot objects to cold ones, but not vice versa. Entropy remains constant in reversible processes and increases in irreversible ones.

Given that reversible processes are theoretical and don't exist in reality, the total entropy of any system plus the entropy of its surroundings always increases during real processes. In other words, any chemical reaction, or a series of interconnected reactions, will naturally proceed in a direction that increases the overall entropy of the universe.

In conclusion, the First Law of Thermodynamics articulates the conservation of energy among processes. In contrast, the Second Law of Thermodynamics governs the direction of spontaneous processes, which proceed toward states of higher total entropy.