Thermodynamics

I

Introduction

Thermodynamics, study of the transformations of energy, which grew out of the analysis of the operation and efficiency of steam engines during the 19th century. It now embraces the whole domain of bulk systems that participate in the conversion of energy from one form to another, including heat engines (devices for converting heat into work), the physical properties of pure materials and mixtures, and chemical reactions. In particular, it is used to optimize the efficiencies of heat engines, to define temperature scales, to establish the criteria for the existence of equilibria between phases, and to predict the spontaneous direction of chemical change. It is essential to the development of electrochemistry (the chemical generation of electrical power) and bioenergetics (the deployment of energy in biochemical reactions). Modern developments include the extension of thermodynamics to include non-equilibrium systems (see Equilibrium).

Classical thermodynamics is concerned with the observed properties of bulk matter and is independent of any microscopic model of matter. It establishes relations between bulk properties, so that measurements of one may be used to infer the value of another. Statistical thermodynamics acknowledges the atomic nature of matter, and is used to express bulk thermodynamic properties to the average behaviour of large assemblies of atoms. Thus, statistical thermodynamics (which is also known as statistical mechanics) provides the link between the properties of individual atoms measured spectroscopically and bulk properties.

II

History

The historical development of thermodynamics is best treated from the viewpoint of its laws, which we consider below. The principal participants include James Joule, who demonstrated the equivalence of heat and work, and Sadi Carnot, who established the criteria for efficiency and opened the way to the formal development of the subject in the hands of William Thomson, 1st Baron Kelvin and Rudolph Clausius.

Thermodynamics remained an esoteric subject for chemists until the work of Willard Gibbs almost single-handedly developed the concepts that enabled it to be applied to chemical phenomena. The establishment of the techniques of statistical thermodynamics is due largely to Ludwig Boltzmann.

The work of these pioneers led to the formulation of four laws: the very fundamental zeroth law was added as an afterthought, hence its somewhat bizarre number. The first three laws (0, 1, and 2) each introduces a fundamental property, namely the temperature, the internal energy, and the entropy, from which the entire edifice of thermodynamics is built. The third law has a somewhat different status from the others.

Throughout the following, we refer to the region of the world of particular interest to us as the system and the rest of the world as the surroundings. Measurements on the system are made in the surroundings. If the system can undergo changes of composition it is termed open; otherwise it is closed. An isolated system is a closed system that cannot exchange energy with its surroundings.

III

The Zeroth Law

The zeroth law establishes the concept of temperature. We need to know that two systems are said to be in thermal equilibrium if, when they are in contact through thermally conducting walls, they undergo no change in properties. It states that if a system A is in thermal equilibrium with system B, and B is in thermal equilibrium with system C, then C and A would also be in thermal equilibrium if they were placed in contact. The implication of this law is the existence of a single intensive (size independent) property that can be used to judge whether any pair of systems would be in thermal equilibrium when placed in contact. That property is the thermodynamic temperature, T.

IV

The First Law

James Joule established the equivalence of heat and work: the same change of state can be brought about by doing work or by supplying the appropriate amount of heat. This equivalence led to the view that heat and work are manifestations of a single quantity, the energy. Specifically, heat and work are modes of transfer of energy that are distinguished only by observations in the surroundings. Work is the transfer of energy that can be used to raise a weight in the surroundings; heat is the transfer of energy that occurs as a result of a temperature difference between the system and its surroundings.

Once inside the system, the energy is stored as internal energy, U, and regardless of the initial mode of transfer can be drawn off in either form. Thus, the system is like a bank, which can accept deposits and transact withdrawals in either currency, but stores its reserves as “energy”. This equivalence is normally expressed by writing the change in internal energy, ΔU, in terms of the energy supplied as work, w, and that supplied as heat, q:

Careful experiments, in particular the demonstration that perpetual motion machines (machines that produce work without consuming fuel) could not be constructed, established the first law of thermodynamics in the form:

The internal energy of an isolated system is constant.

The internal energy—a measure of the total energy stored inside the system—has a simple operational significance: provided the system can do no work (for instance, it has rigid walls and cannot do work by pushing back the atmosphere as it expands), then a change in internal energy is equal to the energy supplied as heat (at constant volume: ΔU = q). This relation is the foundation of calorimetry (the measurement of heat transactions between a system and its surroundings, and their interpretations in terms of the internal energy).

Many processes occur in systems that are free to expand. As a result, not all the energy that enters as heat remains in the system as some is used to do work. Therefore, under these circumstances the change in internal energy is not equal to the energy supplied as heat. To accommodate this difference automatically, the system is described in terms of the enthalpy, H, which is related to the internal energy by

where p is the pressure of the system and V is its volume. Thermodynamic arguments show that a change in enthalpy can be identified with the quantity of energy supplied as heat to a system at constant pressure (at constant pressure: ΔH = q).

The enthalpy is the foundation of thermochemistry—the study of the heat transactions accompanying chemical reactions. A reaction that releases energy as heat and undergoes a reduction of enthalpy (ΔH < 0) is termed exothermic, and one that absorbs heat and increases in enthalpy (ΔH > 0) is termed endothermic. One of the basic laws of thermochemistry is Hess’s Law, which states that the heat released by a reaction is the sum of the heat released by each reaction into which the overall reaction can be regarded as divided. However, this law is a direct consequence of the first law and has no further fundamental significance.

Both the internal energy and the enthalpy of a system increase as the temperature is raised. The slope of each quantity plotted against the temperature is called the heat capacity, C, of the system at constant volume and constant pressure, respectively. Formally:

A high heat capacity indicates that for a given transfer of energy as heat, the temperature rises by only a small amount. Thermodynamic arguments establish a general relation between the two heat capacities of a substance in terms of its compressibility and thermal expansivity. For a perfect gas, the relation is simply

where n is the amount of substance (in moles) and R is the gas constant. This is an example of how thermodynamics provides a relation between different properties of a substance.