Systems of matter

Fig. 2.13), and an external system of matter and energy, respectively. These systems and the resulting interactions are classified in Fig. 3.2. 

The dispersive tendency dominates in a high-temperature system containing only a few particles, while the order tendency is important in a system in which the particles are themselves ordered, as in a crystal or the DNA helix. The real states of systems of matter lie somewhere between these two extremes. 

In the particular case of optical activity I can describe the experiment by choosing % to be the electric polarization operator P(x, t) for the material medium, while tot refers to the combined system of matter interacting with the polarized light beam. Note that [ tot> P] = 0, where P is the space-inversion operator (see40 and Sect. 4). Then the mean value,... 

The mixing of all systems of matter involves a relative displacement of the particles, whether they are molecules, globules, or small crystals, until a state of maximum disorder is created and a completely random arrangement is achieved. 

The interest in alchemy did not exclude philosophical or theoretical aspects of the study of matter, and a number of different systems of matter theory were developed in China. A four-element system based on earth, water, air (or wind), and fire can be traced back to Chinese creation stories, but a more popular system, based on five elements, was well established by the time of the introduction of Taoism, and its roots are lost in history. The five elements of... 

All living things are part of a larger system of matter and energy. 

Here follows illustration of this principle while solving three representative physical systems of matter atomic hydrogen (and hydrogenic atoms), molecules in vibrational states and the solid state of fiee electrons (for clarifications on this linguistically paradox see Section 3.3.3). 

Any atom is formed by a positively charged nucleus surrounded by a negatively charged electron cloud. This structure entails that all atoms and molecules in a system of matter are provided with a surrounding, electrostatic field. By interaction between fields of this kind, attractive or repulsive, intermolecular forces arise. 

The states of matter - solid, liquid, or gaseous - is determined by a balance between two opposite tendencies. The molecules of any system of matter are... 

The temperature of a system of matter, for example a gas, is a measure of the average kinetic energy of its molecules. The higher the temperature in a system of matter, the higher the average kinetic energy of its molecules. This simple physical interpretation of the concept of temperature illustrates at the same time the existence of a lowest temperature, absolute zero, where the molecules are in a state of rest with a minimum of kinetic energy. 

The most important forms of work included in the description of systems of matter will be described in the following. 

In thermodynamics, work contributions are often seen in connection with compression or expansion of systems of matter - the so-called volume work. Assume a system consisting of n moles of an ideal gas confined in a cylinder under a frictionless piston. The gas pressure is denoted p and the piston area is denoted A. To maintain equilibrium in this system the piston is subjected to an external force F = p - A. 

In liquids and solid substances the energy level of the molecules is higher at the surface of the substance than further inside the substance. Therefore, positive work needs to be done on a system to increase its surface area. This surface effect is seen both in liquids and in solid substances. In liquid systems the effect is visible in the form of a surface tension cr in solid substances the effect is not directly visible. This work contribution is an essential quantity in the thermodynamic description of systems of matter with a large specific surface. 

The expression (2.18) can be shown to be universal for the work in the formation of a new surface in systems of matter thus, in conclusion... 

Thermodynamic considerations refer to a predefined system separated from its snrroimdings by an imaginary or real boundary as a whole, the system and its surroundings form the thermodynamic universe (see chapter 2). The following contains a brief explanation of the concept of energy and the energy forms of the thermodynamic system of matter. 

In these examples, the presence of energy - the capacity to do work or to release heat - is evident. However, we cannot base the description of the composition of systems of matter on such more or less intuitive energy considerations. What is for example the energy content in a loaded tensile steel bar - and what does this energy content mean in relation to the physical and chemical properties of the steel, e.g. the resistance to corrosion. Such questions are addressed in the thermodynamic description of substances. 

An energy content can be ascribed to any thermodynamic system of matter -the internal energy U of the system which is boimd up with phenomena in the electronic, atomic and molecular structure of the stem. For systems of matter at room temperature, changes of the internal energy AU will mainly be caused by activation of the following energy forms in the system ... 

The internal energy U in a system of matter can be kinetic energy Ek connected with movement of atoms or molecules. Kinetic energy exists in two qualitatively different forms... 

Macroscopic kinetic energy created by an ordered simultaneous movement of a system of matter, for example in the form of a weight falling down in a gravitational field. The macroscopic kinetic energy of the stem of matter is an often used quantity in calculations within mechanical physics. 

The molecular kinetic energy i is an important quantity in the thermodynamic description of systems of matter any temperature change therefore indicates a change in the average kinetic energy of the molecules. 

Figure 3.3. Molecular kinetic energy is disordered thermal movement of atoms and molecules in a system. Macroscopic kinetic energy is an ordered, simultaneous movement of a system of matter. The temperature of a system of matter is a measure of the average molecular kinetic energy of the atoms and molecules of the system.

The internal energy U is an appropriate state function in the description of processes developing at constant volmne V, since contributions from volume work 5W = —pdV can be omitted. In everyday systems of matter, the majority of reactions, however, develop at a constant atmospheric pressure rather than at constant volume. Therefore, it is an advantage to introduce a modified state function, enthalpy H, which is adjusted to the description of processes developing at constant pressure, i.e. isobaric processes. 

The energy quantities enthalpy H and enthalpy change AH are fundamental calculation parameters in technical calculations of materials. Nearly all calculations deaUng with equilibrium in, or transformations of systems of matter, contain the quantities H and AH. Examples include ... 

Phase equilibria in systems of matter vapom pressiue calculations, freezing and freezing pressure, shrinkage and swelhng mechanisms, vapom pressme over capillary systems, phase diagrams, etc. 

A similar deduction can be made for a system of matter heated at constant volume V in this case, the increase in internal energy AU according to (3.9) is equal to the supplied heat Qi.g, and in accordance with (3.10), cy is introduced into the expression for dU. This results in the following expression for calculation of the entropy change due to heating or cooling of a system of matter. 

A temperature change from Ti to T2 changes the entropy of a system of matter with... 

Phase transformations play an important role within the science of construction materials. Different phenomena such as hardening of steel, freezing damage of concrete, moisture absorption in wood, and chemical shrinkage of hardening cement paste, are all connected with phase transformations in systems of matter. Table 4.1 contains an overview of the most important phase transformations between substances in the solid, liquid, and gaseous states. 

For describing phase equilibrium, the entropy change AS in phase transformations is an important parameter. Therefore, we shall set up an expression to calculate AS for isothermal phase transformations in systems of matter. Normally, a phase transformation will be connected with absorption or release of heat this is known, for example, in the form of the heat of fusion of ice and the heat of evaporation of water. This enthalpy change - the transformation enthalpy ArHr - is a direct measure of the entropy change by the phase transformation concerned. 

It is now assumed that a process occurs at constant pressure p in the system of matter. By the process, the system is brought from the state of equilibrium (1) at (T,p) to the state of equilibrium (2) at (T,p). During the process the surroundings are assumed to be in thermodynamic equilibrium at the temperature T. 

At a given temperature, the number of possible micro states are smaller in a crystal than in a Uquid melting of substances, therefore, is always connected with an increase in entropy. When a substance is transformed from a liquid into a gas, the degree of disorder is increased therefore, an evaporation process is always connected with an increase in entropy. For phase transition in systems of matter, therefore, it generally applies that... 

Generally, for phase transformations in systems of matter, melting and evaporation bring along an increase in entropy, i.e. 

When introduced through the second law (4.12), entropy S is the fundamental parameter for describing the directionality of spontaneous processes and for setting up equilibrimu criteria for systems of matter. However, in order to develop efficient calculation methods it is appropriate to introduce a composed state function, the Gibbs free energy G. In the following it will be shown how the G function in a natural way summarizes the equilibrium criteria developed in Chapter 4. 

The definition of G includes the enthalpy H, which is a particularly suitable energy function for description of changes of state at constant pressure p (see section 3.4). As seen from the following, the G function is also adapted to the description of equilibrium in systems of matter at constant pressure p. 

The equilibrium condition in eqn. (5.7) contains rather fundamental information of the reaction concepts of systems of matter. Any spontaneous reaction reduces the free energy of a system G - the system moves spontaneously towards a state of equilibrium with a minimum of free energy Gmin- For a chemical reaction or phase transformation linking two states of equilibrium, AG is determined by... 

The weighting between these opposite tendencies is determined by the temperature T. At low temperatures, a negative AH contribution will normally be dominating since in this case the quantity TAS is small. Therefore, at low temperatures, systems of matter can typically be found in a state with minimum enthalpy, i.e. condensed in a liquid or a solid state. 

The Clausius-CIapeyron equation shows the following characteristic property at the vapour pressure of the substances. Depicting the logarithm of the equilibrium vapour pressure (p) as ordinate and (1/T) as abscissa results in curves with the slope —AH/R. The curves will be almost rectilinear since AH is only slightly dependent on temperature. Such form of depicting is, for example, useful for experimental determination of AH for phase transformations in systems of matter. 

With introduction of the concept of molar free energy G (J/mol) we have a measure of the tendency of the substances to react or to change state. Any system of matter will spontaneously seek towards an equilibrimn state with a minimiun of free energy G. Therefore, a substance can only be in equilibrium in a system if there is the same molar free energy G all over the system. 

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