Second law of thermodynamics


Historically, the second law of thermodynamics was an empirical finding that was accepted as an axiom of thermodynamic theory. Statistical mechanics, classical or quantum, explains the microscopic origin of the law. The second law has been expressed in many ways. Its first formulation is credited to the French scientist Sadi Carnot, who in 1824 showed that there is an upper limit to the efficiency of conversion of heat to work in a heat engine. This aspect of the second law is also known as Carnot's rule or limit.



The second law of thermodynamics states that the spontaneous processes always proceed in such a way that the entropy of the universe increases.  Entropy refers to the measure of the disorder or randomness of the particles that constitute the system. It is denoted by the symbol-S. The tendency towards disorder is summarized in the law of disorder or simply the second law of thermodynamics.



Predicting changes in Entropy

We need to recall that the change in enthalpy for a reaction is equal to the enthalpy of the products minus the enthalpy of the reactants.


Therefore, if the entropy of the system increase during a process, SPRODUCTS>SREACTANTS and SSYSTEM are positive. Conversely, SPRODUCTS< SREACTANTS if the entropy of a system decreases during a reaction.


Criteria for thermodynamics

Entropy changes when the associated state changes

In solids, molecules are closely packed and have limited movement, but they have some freedom to move to liquids. In gases, molecules move freely except when they are held up in the container. Therefore, we expect an increase in entropy as the substance changes its state from solid into the liquid. The dissolving of gases into solvents leads to a decrease in entropy. Gas particles have more entropy when they can move freely in the gaseous state than when they are dissolved in a liquid or solid that limit`s their movements and randomness.  Let us assume that no change in physical state, the entropy of a system normally increases when the number of gaseous reactant particles. This is because the higher the number of gaseous particles, the more random arrangements are available. With some exceptions, we can very well predict the change in entropy when a solid or liquid dissolves to form the solution. The solute particles which are separated and pure before dissolving become dispersed throughout the solvent. Therefore, dissolution normally increases the randomness and disorder of the particles and the entropy of the system increases.

An increase in the temperature of the substance is always accompanied by an increase in the random motion of particles

We should recall that the kinetic energy of molecules increases with temperature. Increased kinetic energy implies faster movement, more possible arrangements, and increased disorder. Therefore, the entropy of any substance increases as it`s temperature increases, and S > 0. N/B.  Because the universe equals the system plus the surrounding, any change in the entropy of the universe is the total sum of changes occurring in the system and surrounding. So,  SUNIVERSE= SSYSTEM+ SSURROUNDING.  Suniverse tends to be positive for reactions and processes under the following conditions.

  1. The reaction or process is termed exothermic when Ssystem is negative. Here, heat energy is released to the surroundings and leads to a rise in temperature thus increasing the entropy of the surrounding.

  2. The entropy of the system increases, so Ssystem is positive. Thus, exothermic reactions accompanied by an increase in entropy are all spontaneous.


Gibbs Energy change for Spontaneous and non-spontaneous processes.

The Gibbs energy was first put forth by Willard Gibbs when he was defining the relationship between enthalpy and entropy. According to Gibbs, the reactions or processes that take place at constant temperature and pressure is the amount of energy available to do work. In contrast, some entropy is associated with energy that is spread out into the surrounding. The free energy change GSYSTEM, is simply the difference between the system’s change in enthalpy and the product of the Kelvin temperature and the change in entropy.


In case the process takes place under standard conditions, the standard free energy change can be expressed by this equation.


The sign for the free energy change of system, GSYSTEM, tells us whether the reaction/process is spontaneous at constant pressure and temperature. In case the sign of the free energy change of the system is negative, the process/reaction is spontaneous, and if the sign is positive then, the reaction is non-spontaneous.





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