Intensive thermodynamic quantities

The quantities G, //, and S are called extensive thermodynamic functions because the magnitude of the quantity in each case depends on the amount of substance in the system. The change in Gibbs free energy under addition of unit concentration of component / at constant concentrations of the other components is called the partial Gibbs free energy of the /-component, i.e., the chemical potential of the /-component in the system. The chemical potential is an intensive thermodynamic quantity, like temperature and concentrations. The formal definition is... 

To obtain a local quantification of entropy in a nonequilibrium material, consider a continuous system that has gradients in temperature, chemical potential, and other intensive thermodynamic quantities. Fluxes of heat, mass, and other extensive quantities will develop as the system approaches equilibrium. Assume that... 

We shall see that the variables fl and i) are related to the intensive thermodynamic quantities temperature and pressure, respectively. But before completing the picture of how macroscopic thermodynamics emerges from the NVE ensemble, we first have one more equilibration to consider - concentration equilibration. For this case, imagine that the partition between the chambers is perforated and particles are permitted to freely travel from one system to the next. The equilibrium statement for this system is... 

In general an intensive thermodynamic quantity P in a uniform system ... 

This method of breaking down intensive thermodynamic quantities can be applied also to any linear combination of partial molar quantities such as dH/ 9 or A. For an ideal system we can make use of the results of 3 and 4 to obtain the relations set out in table 7.1. 

Tunell, G., 1960, Relations Between Intensive Thermodynamic Quantities and Their First Derivatives in a Binary System of One Phase San Francisco, W.H. Freeman, 47 pp. 

Consider a two-phase system containing the homogeneous phases a and P divided by a flat interface. Each phase is thermodynamically characterized by its variables of state. The crossing over from a to P takes place over a region of finite thickness. In this transition region the intensive thermodynamic quantities change gradually from... 

The solid is pale blue the liquid is an intense blue at low temperatures but the colour fades and becomes greenish due to the presence of NO2 at higher temperatures. The dissociation also limits the precision with which physical properties of the compound can be determined. At 25°C the dissociative equilibrium in the gas phase is characterized by the following thermodynamic quantities ... 

In this book, we will express our thermodynamic quantities in SI units as much as possible. Thus, length will be expressed in meters (m), mass in kilograms (kg), time in seconds (s), temperature in Kelvins (K), electric current in amperes (A), amount in moles (mol), and luminous intensity in candella (cd). Related units are cubic meters (m3) for volume, Pascals (Pa) for pressure. Joules (J) for energy, and Newtons (N) for force. The gas constant R in SI units has the value of 8.314510 J K l - mol-1, and this is the value we will use almost exclusively in our calculations. 

The advantage of the chemical potential over the other thermodynamic quantities, U, H, and G, is that it is an intensive quantity—that is, is independent of the number of moles or quantity of species present. Internal energy, enthalpy, free energy, and entropy are all extensive variables. Their values depend on the extent of the system—that is, how much there is. We will see in the next section that intensive variables such as p., T, and P are useful in defining equilibrium. 

The conditions for eqnilibrinm have not changed, and application of the phase rnle is conducted as in the previous section. The difference now is that composition can be counted as an intensive variable. Composition is accounted for through direct introduction into the thermodynamic quantities of enthalpy and entropy. The free energy of a mixtnre of two pure elements, A and B, is still given by the definition... 

Name three extensive and three intensive properties that relate to thermodynamic quantities. What is the basic difference between the two types of properties ... 

Of the thermodynamic quantities just mentioned, only the determination of the expansion coefficient or other quantities reflecting its change have assumed practical importance for the identification of secondary transitions in glassy polymers. The most efficient methods for the investigation of the dynamics and intensity of molecular motions have so far been those based on the interference between molecular motion and the oscillating magnetic, electric or mechanical force field. In recent years, methods which employ various probes or labels in the study of molecular mobility have increasingly been used. 

Here, 7s is called the generalized surface intensive parameter or surface energy. 7s is not a real thermodynamic quantity since it depends on the history of the solid [325]. It depends... 

These quantities (V and p) are independent of the size of a system, and are examples of intensive thermodynamic variables. Tlrey are functions of the temperature, pressure, and composition of a system, additional quantities tlrat are independent of system size. 

Partial molar quantities are intensive thermodynamic functions. For example, the partial molar volume is the increase of the volume per mole of component i when the number of moles of i are modified with an infinitesimal amount. Thus, the partial molar volume of component i is given by the expression ... 

The electron in H O becomes fully hydrated in ps time to become a discrete chemical species with a known charge (—1), ionic conductivity (190 cm 0 and diffusion coefficient (4.9 X 10 cm s )- From estimates of its thermodynamic quantities, the standard redox potential of [e ] is ca. —2.87 V, making it a powerful reducing agent. Because of its intense and broad optical absorption spectrum, (A = 710 nm ma. = cm ) extending from the UV into the ir and its relatively long... 

The partial pressures of the species in gaseous aluminium-selenium mixtures were determined in the temperature range 1232 to 1352 K using mass spectrometry and Knud-sen effusion cells. The measured ion intensities were converted to partial pressures by normalising the ion intensity of Al(g) in equilibrium with Al(l) to the known total vapour pressure. The derived thermodynamic quantities were recalculated by the review using the selected thermodynamic properties of Se2(g), the CODATA [89COX/WAG] properties of Al(g), and the entropies and heat capacity expressions of the aluminium selenides given in Sections V.8.2.1.1 to V.8.2.1.3. The results are summarised in Table A-59. 

Thermodynamic quantities which have the same value throughout a homogeneous compartment (temperature, T pressure, p) are called intensive. Those which are proportional to the amount of component i in that compartment are called extensive (enthalpy, H entropy. S free-energy, G). An extensive quantity may be converted to an intensive one by dividing by the amount of component i present. For example, the partial molal free-energy or chemical potential. 

When N-dependent errors are feared, one procedure has been to do the Monte Carlo work for several sample sizes N, afterwards extrapolating to the large-system limit (l/N- 0). This extrapolation (of intensive thermodynamic or structural quantities, such as U/N or g2) has usually been done linearly in 1/N (cf. Card and Valleau, Rasaiah et but that is not entirely... 

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