Entropy extensive

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. 

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. 

We will now show that the form of Sdis ( ) in the gap has no relevance to the physics of the problem. Therefore, the entropy extension over the gap can be arbitrary as long as Sdis ( ) is continuous and concave. We consider quantities associated with communal entropies in this section, but will not show comm for simplicity of notation. The argument can be easily extended to configurational entropies. We compare Zdis(T) and Z T). They only differ in terms containing E < Ek- For E > k, they use the same function Sdis( ). Thus, for T > TKOr( dis(T) > k), the two PFs are identical. Consider T = Tk and write... 

A general prerequisite for the existence of a stable interface between two phases is that the free energy of formation of the interface be positive were it negative or zero, fluctuations would lead to complete dispersion of one phase in another. As implied, thermodynamics constitutes an important discipline within the general subject. It is one in which surface area joins the usual extensive quantities of mass and volume and in which surface tension and surface composition join the usual intensive quantities of pressure, temperature, and bulk composition. The thermodynamic functions of free energy, enthalpy and entropy can be defined for an interface as well as for a bulk portion of matter. Chapters II and ni are based on a rich history of thermodynamic studies of the liquid interface. The phase behavior of liquid films enters in Chapter IV, and the electrical potential and charge are added as thermodynamic variables in Chapter V. 

In other words, if we look at any phase-space volume element, the rate of incoming state points should equal the rate of outflow. This requires that be a fiinction of the constants of the motion, and especially Q=Q i). Equilibrium also implies d(/)/dt = 0 for any /. The extension of the above equations to nonequilibriiim ensembles requires a consideration of entropy production, the method of controlling energy dissipation (diennostatting) and the consequent non-Liouville nature of the time evolution [35]. 

When g = 1 the extensivity of the entropy can be used to derive the Boltzmann entropy equation 5 = fc In W in the microcanonical ensemble. When g 1, it is the odd property that the generalization of the entropy Sq is not extensive that leads to the peculiar form of the probability distribution. The non-extensivity of Sq has led to speculation that Tsallis statistics may be applicable to gravitational systems where interaction length scales comparable to the system size violate the assumptions underlying Gibbs-Boltzmann statistics. [4]... 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

The heat capacities and entropies of organic compounds, including many thiols, have been compiled (19,20). The thermochemistry of thiols and other organosulfur compounds has been extensively reviewed (21). 

Thermodynamic data on H2, the mixed hydrogen—deuterium molecule [13983-20-5] HD, and D2, including values for entropy, enthalpy, free energy, and specific heat have been tabulated (16). Extensive PVT data are also presented in Reference 16 as are data on the equihbrium—temperature... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Extension of Generalized Charts. In 1975, the usehilness of generalized charts was extended upon the pubtication of extensive tables of residual enthalpy, entropy, and heat capacity (82). This tabular data has also been converted into graphical form (3). The corresponding equations incorporate the acentric i2iC. or.PesiduaIenthalpy. 

Thus the extensive variables characterizing the lamellar system are entropy [Pg.6]

Loss of motivity (dissipation of energy) is therefore accompanied by increase of entropy, but the two changes are not wholly co-extensive, because the former is less the lower the temperature T0 of the auxiliary medium, whilst the latter is independent of T0, and depends only on the temperature of the parts of the system. If T0 = 0, i.e., the temperature of the surroundings is absolute zero, there is no loss of motivity, whilst the entropy goes on increasing without limit as the heat is gradually conducted to colder bodies. 

Entropy is an extensive property and Sm the molar entropy is often used. 

Since we expect entropy to be extensive and behave like the other extensive thermodynamic properties, the integration constant must be equal to zero so that... 

Doubling the number of molecules increases the number of microstates from W to W2, and so the entropy changes from k In W to k In W2, or 2k In W. Therefore, the statistical entropy, like the thermodynamic entropy, is an extensive property. 

Standard Gibbs free energies of formation can be determined in various ways. One straightforward way is to combine standard enthalpy and entropy data from tables such as Tables 6.5 and 7.3. A list of values for several common substances is given in Table 7.7, and a more extensive one appears in Appendix 2A. 

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