Work and the State of a System

Thermodynamics involves work and heat. It began in the 19th century with the efforts of engineers to increase the efficiency of steam engines, but it has become the general theory of the macroscopic behavior of matter at equilibrium. It is based on empirical laws, as is classical mechanics. Although classical mechanics has been superseded by relativistic mechanics and quantum mechanics, thermodynamics is an unchallenged theory. No exceptions have been found to the laws of thermodynamics. 

Nicolas Leonard Sadi Carnot, 1796-1832, was a French engineer who was the first to consider quantitatively the Interconversion of work and heat and who Is credited with founding the science of thermodynamics. 

Gaspardde Coriolis, 1792-1843, was a French physicist best known for the Coriolis force. 

The quantitative measurement of work was introduced by CamoL who defined an amount of work done on an object as the height it is lifted times its weight. This definition was extended by Coriolis, who provided the presently used definition of work The amount of work done on an object equals the force exerted on it times the distance it is moved in the direction of the force. If a force Fj is exerted on an object in the z direction, the work done on the object in an infinitesimal displacement dz in the z direction is 

If the force and the displacement are not in the same direction, they must be treated as vectors. A vector is a quantity that has both magnitude and direction. Vectors are discussed briefly in Appendix B. We denote vectors by boldface letters and denote the magnitude of a vector by the symbol for the vector between vertical bars or by the letter in plain type. The amount of work dw can be written as the scalar product of the two vectors F and dr where F is the force exerted on the object and dr is its displacement  

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Note that the maximum work depends only upon the initial and final states of a system and not upon the path. 

Heat, like work, is energy in transit and is not a function of the state of a system. Heat and work are interconvertible. A steam engine is an example of a machine designed to convert heat into work.h The turning of a paddle wheel in a tank of water to produce heat from friction represents the reverse process, the conversion of work into heat. 

For these and other phenomena, thermal and work quantities, although controUing factors, are only of indirect interest. Accordingly, a more refined formulation of thermodynamic principles was established, particularly by Gibbs [6] and, later, independently by Planck [7], that emphasized the nature and use of several special functions or potentials to describe the state of a system. These functions have proved convenient and powerful in prescribing the rules that govern chemical and physical transitions. Therefore, in a sense, the name energetics is more descriptive than is... 

Therefore, it seems appropriate to define a quantity, the energy U, whose value is characteristic of the state of a system, whereby the adiabatic work required to bring about a change of state is equal to the difference between the value of t/ in one state and that in another state. That is. 

The first law of thermodynamics, which can be stated in various ways, enuciates the principle of the conservation of energy. In the present context, its most important application is in the calculation of the heat evolved or absorbed when a given chemical reaction takes place. Certain thermodynamic properties known as state functions are used to define equilibrium states and these properties depend only on the present state of the system and not on its history, that is the route by which it reached that state. The definition of a sufficient number of thermodynamic state functions serves to fix the state of a system for example, the state of a given mass of a pure gas is defined if the pressure and temperature are fixed. When a system undergoes some change from state 1 to state 2 in which a quantity of heat, Q, is absorbed and an amount of work, W, is done on the system, the first law may be written... 

A thermodynamic system (closed system) is one that interacts with the surroundings by exchanging heat and work thru its boundary an isolated system is one that does not interact with the surroundings. The state of a system is determined by the values of its various properties, eg, pressure, volume, internal energy, etc. A system can be composed of a finite number of homogeneous parts, called phases, or there can be a single phase. For some applications, it may... 

We see from these equations that we deal with a large number of variables in thermodynamics. These variables are E, S, H, A, G, P, V, T, each nh and two variables for each additional work term. In any given thermodynamic problem only some of these variables are independent, and the rest are dependent. The question of how many independent variables are necessary to define completely the state of a system is discussed in Chapter 5. For the present we take the number of moles f each component, the generalized coordinate associated with each additional work term, and two of the four variables S, T, P, and V as the independent variables. Moreover, not all of... 

We conclude this chapter by going back to Albert Einstein, whose work was instrumental in the evolution of the quantum theory. Einstein was unable to tolerate the limitations on classical determinism that seem to be an inevitable consequence of the developments outlined in this chapter, and he worked for many years to construct paradoxes which would overthrow it. For example, quantum mechanics predicts that measurement of the state of a system at one position changes the state everywhere else immediately. Thus the change propagates faster than the speed of light—in violation of at least the spirit of relativity. Only in the last few years has it been possible to do the appropriate experiments to test this ERPparadox (named for Einstein, Rosen and Podolsky, the authors of the paper which proposed it). The predictions of quantum mechanics turn out to be correct. 

The macroscopic state of any one-component fluid system in equilibrium can be described by just three properties, of which at least one is extensive. All other properties of the state of the same system are necessarily specified by the chosen three properties. For instance, if for a single component gas in equilibrium, pressure, temperature, and volume are known, all other properties which describe the state of that gas (such as number of moles, internal energy, enthalpy, entropy, and Gibbs energy) must have a specific single value. Since the state of a system can be described exactly by specific properties, it is not necessary to know how the state was formed or what reaction pathway brought a state into being. Such properties that describe the state of a system are called slate functions. Properties that do not describe the state of a system, but depend upon the pathway used to achieve any state, are called path functions. Work and heat are examples of path functions. 

In Section IV.C, we took advantage of the relationship between C(t) and an effective reversible work, W git), to constrain the state of a system at time t. In effect, we gradually applied this constraint to the ensemble of trajectories of length t that begin in state A, obtaining a new ensemble of reactive trajectories. Here, we consider a different process connecting the same two ensembles of trajectories. Because this process is also reversible, it involves the same work In the new process, trajectories of length > t that... 

To understand why certain processes are spontaneous, we need to consider more closely the ways in which the state of a system can change. Recall from Section 5.2 that quantities such as temperature, internal energy, and enthalpy are state functions., properties that define a state and do not depend on how we reach that state. The heat transferred between a system and its surroundings, q, and the work done by or on the sjrstem, w, are not state functions—their values depend on the specific path taken between states. One key to imderstanding spontaneity is understanding differences in the paths between states. 

The exergy of a system is defined as the maximum useful work available from a process depending on the reference state of its surroundings. It depends on the physical, chemical, and thermal state of a system [24] and can be calculated by ... 

Thermodynamic properties are characteristics of a system (e.g., pressure, temperature, density, specific volume, enthalpy, entropy, etc.). Because properties depend only on the state of a system, they are said to be path independent (unlike heat and work). Extensive properties are mass dependent (e.g., total system energy and system mass), whereas intensive properties are independent of mass (e.g., temperature and pressure). Specific properties are intensive properties that represent extensive properties divided by the system mass, for example, specific enthalpy is enthalpy per unit mass, h = H/m. In order to apply thermodynamic balance equations, it is necessary to develop thermodynamic property relationships. Properties of certain idealized substances (incompressible liquids and ideal gases with constant specific heats) can be calculated with simple equations of state however, in general, properties require the use of tabulated data or computer solutions of generalized equations of state. 

Fluctuations connect the states of a system by accident. By contrast, when variables are fine-tuned and coordinated with heat and work exchanges, the states are linked by design. We consider a special type of design, one that defines a locus of nearest-neighbor state points. The sequence of points marks a pathway in the manner of a... 

The state of a system is defined by variables such as composition, volume, temperature, and pressure. The change in a state function for a system depends only on the initial and final states of the system, and not on the path by which the change is accomplished. Energy is a state function work and heat are not. 

At the same time, significant changes in the state of a system can result from fairly moderate deviations in T, for example, the changes in the mutual solubility of both the disperse phase and the dispersion medium components, leading to a radical decrease in a. Typical examples include studies on systems approaching the critical point, (and yet still below the TJ, such as those carried out with binary mixtures of paraffins with moderately polar organic substances, such as oxyquinoline [26,67,68], In these works, the formation of direct, inverse, and bicontinuous microemulsions had been described and analyzed in comparison with the independently determined values of a down to 10" -10" mN/m,... 

In words, the increase (or decrease) in enthalpy is equal to the heat absorbed (or evolved) when the process occurs at constant pressure and the only work is P AV. As with E, no attempt is made to define absolute values of H for a system. Of interest, rather, is the change in H that occurs when the state of a system is changed at constant pressure. 

One-, two-, and three-component systems will be considered. A one-component system is one substance that defines composition uniquely throughout a diagram. Temperature and/or pressure are usually the variables under consideration to define the state of a system. In phase transition work, variables such as density, heat capacity, optical properties, etc. may be measured to determine changes in phase state as the variables of state are changed. If there are no transitions in a one-component system in a region under consideration, there is very limited phase chemistry as such. 

The state of a system represents the condition of the system as defined by the properties. Properties are macroscopic quantities that are perceived by our senses and can be measured by instruments. A quantity is defined as the property if it depends only on the state of fhe system and independent of the process by which it has reached at the state. Some of the common thermodynamic properties are pressure, temperature, mass, volume, and energy. Properties are also classified as infensive and exfensive. Infensive properties are independent of fhe mass of fhe system and a few examples of this include pressure, temperature, specific volume, specific enthalpy, and specific entropy. Extensive properties depend on the mass of the system. All properties of a system at a given state are fixed. For a system that involves only one mode of work, fwo independent properties are essential to define the thermodynamic state of fhe system and the rest of the thermodynamic properties can be determined on the basis of fhe fwo known independent properties and using thermodynamic relations. For example, if pressure and temperature of a system are known, the state of fhe system is then defined. All other properties such as specific volume, enthalpy, internal energy, and entropy can be determined through the equation of state and thermodynamic relations. 

Various theoretical treatments have been advocated for studying chemical dynamics and the present work will highlight some important results that can be obtained using non-relativistic quantum mechanics. In the absence of an external field, the state of a system composed of Ng... 

The energy of a system can be changed by means of thermal energy or work energy, but a further possibility is to add or subtract moles of various substances to or from the system. The free energy of a pure substance depends upon its chemical nature, its quantity (AG is an extensive property), its state (solid, liquid or gas), and temperature and pressure. Gibbs called the partial molar free heat content (free energy) of the component of a system its chemical potential... 

We now suppose that a system undergoes any change, and that no energy changes occur outside the system except the disappearance of a quantity of heat Q and the performance of a quantity of work A. If the final state is the same as the initial state, the process must, by definition, have been a cyclic process, and hence... 

Clerk Maxwell (South Kensington Conferences, 1876), in discussing the work of Willard Gibbs, remarked that the existence of a system depends on the magnitudes of the system, which are the quantities of the components, the volumes, the entropies, as well as on the intensities of the system, viz., the temperature and the potentials of the components (cf. 143). In his Theory of Heat he also refers to a separation of the variables in terms of which the state can be defined into two classes, one of which includes what are called intensities (pressure, temperature), and the other magnitudes (volume, entropy). 

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