Forces, Energy, and Work

The aim of this appendix is to describe a simple model that will help to clarify the meaning of energy and mechanical work in macroscopic systems. The appendix applies fundamental principles of classical mechanics to a collection of material particles representing a closed system and its surroundings. Although classical mechanics cannot dupUcate all features of a chemical system—for instance, quantum properties of atoms are ignored—the behavior of the particles and their interactions will show us how to evaluate the thermodynamic work in a real system. 

In broad outline the derivation is as follows. An inertial reference frame in which Newton s laws of motion are valid is used to describe the positions and velocities of the particles. The particles are assumed to exert central forces on one another, such that between any two particles the force is a function only of the interparticle distance and is directed along the line between the particles. 

We define the kinetic energy of the collection of particles as the sum for all particles of (where m is mass and v is velocity). We define the potential energy as the sum over pairwise particle-particle interactions of potential functions that depend only on the interparticle distances. The total energy is the sum of the kinetic and potential energies. With these definitions and Newton s laws, a series of mathematical operations leads to the principle of the conservation of energy the total energy remains constant over time. 

A similar derivation, using a slightly different notation, is given in Ref. [43]. 

A material particle is a body that has mass and is so small that it behaves as a point, without rotational energy or internal structure. We assume each particle has a constant mass, ignoring relativistic effects that are important only when the particle moves at a speed close to the speed of light. 

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APPENDIX G FORCES, ENERGY, AND WORK G.l Forces BETWEEN Particles... 

The first law of thermodynamics states that energy may be converted between forms, but cannot be created or destroyed. Joule was a superb experimentalist, and performed various types of work, each time generating energy in the form of heat. In one set of experiments, for example, he rotated small paddles immersed in a water trough and noted the rise in temperature. This experiment was apparently performed publicly in St Anne s Square, Manchester. Joule discerned a relationship between energy and work (symbol w). We have to perform thermodynamic work to increase the pressure within the tyre. Such work is performed every time a system alters its volume against an opposing pressure or force, or alters the pressure of a system housed within a constant volume. 

Energy and work have units of force time distance, such as a Joule, which is a Newton metre. Energy is sometimes measured as the amount of heat that must be transferred to a specified mass of water to raise the temperature of the water at a specified temperature interval at a specified pressure (e.g. 1 kcal corresponds to raising 1 kilogramme of water from 15 to 16°C). 

The study of thermodynamics involves mechanical variables such as force, pressure, and work, and thermal variables such as temperature and energy. Over the years many definitions and units for each of these variables have been proposed for example, there are several values of the calorie, British thermal unit, and horsepower. Also, whole... 

A factory is a local grouping of production factors for the realization of the entire or a part of the value chain of real goods. The main production factors are material, facilities, work force, energy, and information. 

The design of heat and mass transfer operations in chemical engineering is based on the well-known correlations that use the dimensionless numbers Nu (Nusselt) for heat transfer and Sh (Sherwood) for mass transfer By balancing the acting forces, energies, and mass flows within the boundary layers of velocity, temperature, and concentration, the theoretical derivation of general relations for Nu and Sh is given in fundamental work [35]. 

Because moment of force (bending moment) and torque are equal to a force times a distance (moment arm or lever arm), their SI unit is N m. The Joule (J = N m), which is a special name for the SI unit of energy and work, should... 

The magnitudes of forces responsible for adhesion (van der Waals, acid-base) can generally be related to fundamental thermodynamics quantities, such as surface free energies and work of adhesion. The work required to separate reversibly the interface between two bulk phases, 1 and 2, from their equilibrium interacting distance to infinite one (Dupre 1869), represented on O Fig. 3.3, is termed work of adhesion and is equal to ... 

To reflect the contribution of the fundamental nature of the long-range interaction forces across the interface, it was suggested (Fowkes 1964) that surface free energies and work of adhesion may be expressed (O Eq. 3.11) by the sum of two terms the first one representative of London s dispersion interactions (superscript D) and the second representative of nondispersion forces (superscript ND), this latter include Debye induction forces, Keesom orientation forces, and acid—base interactions. 

Energy balances can be more difficult because energy and work can take so many different forms. Internal, kinetic, potential, chemical, and surface energies are all important. Work can involve forces of pressure, gravity, and electrical potential. As a result, a truly general energy balance is extraordinarily complicated, so much so that it is difficult to use. 

Relationship between the force and potential work-energy theorem). In order to establish a relationship between energy and work we shall consider a body in a stationary field. Acquire an elementary body s displacement dl. The internal forces of the field will produce the work dA equal to the potential energy change (dA= -dU). Therefore,... 

The cleaning process proceeds by one of three primary mechanisms solubilization, emulsification, and roll-up [229]. In solubilization the oily phase partitions into surfactant micelles that desorb from the solid surface and diffuse into the bulk. As mentioned above, there is a body of theoretical work on solubilization [146, 147] and numerous experimental studies by a variety of spectroscopic techniques [143-145,230]. Emulsification involves the formation and removal of an emulsion at the oil-water interface the removal step may involve hydrodynamic as well as surface chemical forces. Emulsion formation is covered in Chapter XIV. In roll-up the surfactant reduces the contact angle of the liquid soil or the surface free energy of a solid particle aiding its detachment and subsequent removal by hydrodynamic forces. Adam and Stevenson s beautiful photographs illustrate roll-up of lanoline on wood fibers [231]. In order to achieve roll-up, one requires the surface free energies for soil detachment illustrated in Fig. XIII-14 to obey... 

The problems that occur when one tries to estimate affinity in terms of component terms do not arise when perturbation methods are used with simulations in order to compute potentials of mean force or free energies for molecular transformations simulations use a simple physical force field and thereby implicitly include all component terms discussed earlier. We have used the molecular transformation approach to compute binding affinities from these first principles [14]. The basic approach had been introduced in early work, in which we studied the affinity of xenon for myoglobin [11]. The procedure was to gradually decrease the interactions between xenon atom and protein, and compute the free energy change by standard perturbation methods, cf. (10). An (issential component is to impose a restraint on the... 

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