What is Thermodynamics?

When a system is not in equilibrium, the system will change until it reaches equilibrium. This process, in which energy is released as a system changes, is a spontaneous change, or spontaneous process. A spontaneous process can be reversible or irreversible. For example, compressing gas in a chamber is a reversible process. When the size of the chamber is expanded and contracted, the gas changes from less compressed to more compressed and back again. However, releasing the gas from the chamber to the atmosphere is an irreversible process. Once the gas is out, it is impossible to collect it and put it back in the chamber. Releasing the gas into another part of a closed system, however, can be reversed with a vacuum pump. In contrast to a spontaneous process, in a nonspontaneous change, or nonspontaneous process, energy must be added to the system for the change to occur. In chemistry, spontaneous and nonspontaneous processes generally refer to chemical reactions. A spontaneous reaction will occur provided the reactants are present. A nonspontaneous reaction will not occur without some input of energy from outside the system, such as thermal energy, electrical energy, or chemical energy. Many chemical reactions are spontaneous in one direction but not the other, such as the oxidation of iron, or rusting. Iron(III) oxide will spontaneously form from iron and water in air, but iron, water, and air will not spontaneously form from iron(III) oxide. In other words, iron rusts in the presence of water and oxygen, but rust does not spontaneously turn back into iron, water, and air. A nonspontaneous reaction requires energy input, but the spontaneity of a reaction is not determined by whether or not it requires an input of energy to proceed. The change in Gibbs free energy of a system, which is the energy available to the system to do work, indicates whether a reaction is spontaneous.

When discussing thermodynamics, it is important to understand the concept of entropy. Entropy (S) is a measure of the disorder of a system. For example, a tower of blocks arranged one on top of the other has low entropy. There is little disorder: each block sits on top of another block, except for the bottom block, which sits on the ground. There is little uncertainty: below each block is another block, except for the ground beneath the bottom block. A toppling tower of blocks has high entropy. There is much disorder: each block's position relative to the other blocks and the ground is difficult to describe. There is uncertainty; the relationships between the positions of the blocks are random.

In real-world systems, macroscopic properties, such as temperature, pressure, volume, density, velocity, and mass, can be measured. The combination of these measurable macroscopic properties of a system is called the macrostate. Entropy describes how organized a system is as defined by microstates. A microstate is a possible energy and positional configuration of the particles of a system. Microstates represent probabilities; the exact positions and velocities of the molecules involved cannot be known, but probabilities for them can be known.

Consider measuring the temperature of a flask of water. It is impossible to measure the temperature of every water molecule. The temperature that is measured, a macrostate, is a measure of the average kinetic energy of all the molecules. Each possible energy configuration is a different microstate. As temperature increases, the number of microstates, possible energy configurations, also increases. The number of microstates is influenced by other macrostates as well. Ludwig Boltzmann, an Austrian physicist and philosopher, developed an equation around 1872 that uses the number of microstates to calculate entropy: In this formula, S is entropy, in joules per kelvin (J/K), k is the Boltzmann constant, which is $1.38\;\times\;10^{-23}\;{\rm J/K,}$ ln is the natural logarithm, and W is the number of microstates. To understand entropy and microstates, consider a system of four particles enclosed in a glass container. The container consists of two bulbs connected by a thin tube, and the particles can freely move between the two bulbs. Consider the different ways the particles can be distributed in the system. All four particles can be in one bulb and none in the other. Or three particles can be in one bulb and one in the other bulb. Alternatively two particles can be in each bulb. Each distribution of the particles in the container is a microstate of the system. This simple system depends only on the position of each particle, so the number of microstates can be calculated by aⁿ, where a is the number of positions possible and n is the number of particles. Therefore the system consisting of four particles, each with two possible positions, has 2⁴, or 16, possible microstates. Using Boltzmann's equation the number of microstates can be used to calculate the entropy of this system. Notice that several of these microstates are identical to each other, varying only in which particle is in each container. Each collection of microstates that have identical distributions is an arrangement. Five arrangements exist in this system:

• Arrangement A: four particles in the left bulb and none in the right; there is one microstate with this arrangement
• Arrangement B: three particles in the left bulb and one in the right; there are four microstates with this arrangement
• Arrangement C: two particles in each bulb; there are six microstates with this arrangement
• Arrangement D: one particle in the left bulb and three in the right; there are four microstates with this arrangement
• Arrangement E: no particles in the left bulb and four in the right; there is one microstate with this arrangement

The probability for the system to be in arrangement A is 1 in 16, or 6.25%, and the probability for arrangement E is also 6.25%. The probability that the system is in arrangement B is 4 in 16, or 25%, and the probability for arrangement D is also 25%. The probability for arrangement C is 6 in 16, or 37.5%.

This simple system shows that the most probable state of the system has the particles distributed evenly between the two containers. However, real systems have many more than four particles, and they have many more than two ways the particles can be arranged and energy values of the particles. As the number of particles increases, the number of microstates becomes uncountably large. The probability of the system being in the state in which the particles are evenly distributed becomes so large that all other possibilities can be disregarded.

When considering chemical reactions, an analysis of the reactants and products allows scientists to predict whether the change in entropy for the reaction is positive or negative. If only gases are involved in the reaction, then the number of moles of reactants and products can be used to determine the sign of the entropy change. If the number of moles of products is less than the number of moles than the reactants, then entropy is negative. The reverse is also true. If the reaction involves multiple states of matter, then the side of the reaction with the gas typically has higher entropy than the side without.

For example, in the reaction $2{\rm {H}_{2}}(g)+{\rm O}_{2}(g)\rightarrow 2{\rm H_{2}{O}}(g)$, there are more moles on the reactants side than the products side, so the change in entropy is negative.

In the reaction $2{\rm {H_2}{O}_{2}}(l)\rightarrow 2{\rm {H}_{2}O}(l)+{\rm {O}_{2}}(g)$, the gas is present on the product side, so the change in entropy is positive.