# Thermodynamics Photo by: Laurentiu Iordache

Thermodynamics is the science of heat and temperature and, in particular, of the laws governing the conversion of thermal energy into mechanical, electrical, or other forms of energy. It is a central branch of science that has important applications in chemistry, physics, biology, and engineering. Thermodynamics is a logical discipline that organizes the information obtained from experiments performed on systems and enables us to draw conclusions, without further experimentation, about other properties of the system. It allows us to predict whether a reaction will proceed and what the maximum yield might be.

Thermodynamics is a macroscopic science that deals with such properties as pressure, temperature, and volume. Unlike quantum mechanics , thermodynamics is not based on a specific model, and therefore it is unaffected by our changing concepts of atoms and molecules. By the same token, equations derived from thermodynamics do not provide us with molecular interpretations of complex phenomena. Furthermore, thermodynamics tells us nothing about the rate of a process except its likelihood.

Applications of thermodynamics are based on three fundamental laws that deal with energy and entropy changes. The laws of thermodynamics cannot be derived; their validity is based on the fact that they predict changes that are consistent with experimental observations.

The first law of thermodynamics is based on the law of conservation of energy, which states that energy can neither be created nor destroyed; therefore, the total energy of the universe is constant. It is convenient for scientists to divide the universe into two parts: the system (the part of the universe that is under study—for example, a beaker of solution) and the surroundings (the rest of the universe). For any process, then, the change in the energy of the universe is zero. Chemists are usually interested only in what happens to the system. Consequently, for a given process the first law can be expressed as

Δ U = q + w          (1)

where Δ U is the change in the internal energy of the system, q is the heat exchange between the system and the surroundings, and w is the work done by the system or performed on the system by the surroundings. The first law is useful in studying the energetics of physical processes, such as the melting or boiling of a substance, and chemical reactions—for example, combustion . The heat change occurring as part of a process is measured with a calorimeter. For a constant-volume process, the heat change is equated to the change in the internal energy Δ U of the system; for a constant-pressure process, which is more common, the heat change is equated to the change in the enthalpy Δ H of the system. Enthalpy H is a thermodynamic function closely related to the internal energy of the system, and is defined as

H = U + PV          (2)

where P and V are the pressure and volume of the system, respectively.

The first law of thermodynamics deals only with energy changes and cannot predict the direction of a process. It asks, for example: Under a given set of conditions of pressure, temperature, and concentration, will a specific reaction occur? To answer the question we need a new thermodynamic function called entropy S. To define entropy, we need to use a quantum mechanical concept. The entropy of a system is related to the distribution of energy among the available molecular energy levels at a given temperature. The greater the number of energy levels that have significant occupation, the greater the entropy.

The second law of thermodynamics states that the entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process. The mathematical statement of the second law of thermodynamics is given by

Δ S univ = Δ S sys + Δ S surr ≥ 0          (3)

where the subscripts denote the universe, the system, and the surroundings, respectively. The greater than portion of the "greater than or equal to" sign corresponds to a spontaneous process, and the equal portion corresponds to a system at equilibrium. Because processes in the real world are spontaneous, the entropy of the universe therefore constantly increases with time.

As is not the case with energy and enthalpy , it is possible to determine the absolute value of entropy of a system. To measure the entropy of a substance at room temperature, it is necessary to add up entropy from the absolute zero up to 25°C (77°F). However, the absolute zero is unattainable in practice. This dilemma is resolved by applying the third law of thermodynamics, which states that the entropy of a pure, perfect crystalline substance is zero at the absolute zero of temperature. The increase in entropy from the lowest reachable temperature upward can then be determined from heat capacity measurements and enthalpy changes due to phase transitions.

Because it is inconvenient to use the change in entropy of the universe to determine the direction of a reaction, an additional thermodynamic function, called the Gibbs free energy ( G ), is introduced to help chemists to focus only on the system. The Gibbs free energy of a system is defined as G = H − TS , where T is the absolute temperature. At constant temperature and pressure, Δ G is negative for a spontaneous process, is positive for an unfavorable process, and equals zero for a system at equilibrium. The change in Gibbs free energy can be related to the changes in enthalpy and entropy of a reaction, and also to the equilibrium constant of the reaction, according to the equation Δ G ° = − RT ln K , where Δ G ° is the change in Gibbs free energy under standard-state conditions (1 bar), R is the gas constant, and K is the equilibrium constant.

Many chemical reactions can be classified as either kinetically controlled or thermodynamically controlled. In a kinetically controlled process the products are thermodynamically more stable than the reactants, hence the reaction is favorable. However, the rate of reaction is often very slow due to a high activation energy barrier. The conversion of the less stable allotropic form of carbon, diamond, to the more stable graphite is an example: The process can take millions of years to complete. In a thermodynamically controlled reaction the reactants may have a number of kinetically accessible routes to follow to form different products, but what is eventually formed is governed by relative thermodynamic stability. In protein folding, for example, a denatured protein may have many possibilities of intermediate conformation; however, the conformation it finally assumes, which corresponds to the physiologically functioning protein, is the most stable state thermodynamically.

Raymond Chang

## Bibliography

Bent, Henry A. (1965). The Second Law: An Introduction to Classical and Statistical Thermodynamics. New York: Oxford University Press.

Berry, R. Stephen (1991). Understanding Energy: Energy, Entropy, and Thermodynamics for Everyman. River Edge, NJ: World Scientific.

Smith, E. Brian (1990). Basic Chemical Thermodynamics , 4th edition. New York: Oxford University Press.