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Clausius

Clapeyron-Clausius equation A thermodynamic equation applying to any two-phase equilibrium for a pure substance. The equation states ... [Pg.101]

Clausius-Clapeyron equation See Clapeyron-Clausius equation. [Pg.102]

Clausius-Mosottf Jaw The molecular polarization (P) of a substance of molecular weight M, density d and dielectric constant O is ... [Pg.102]

The existence of intennolecular interactions is apparent from elementary experimental observations. There must be attractive forces because otherwise condensed phases would not fomi, gases would not liquefy, and liquids would not solidify. There must be short-range repulsive interactions because otherwise solids and liquids could be compressed to much smaller volumes with ease. The kernel of these notions was fomuilated in the late eighteenth century, and Clausius made a clear statement along the lines of this paragraph as early as 1857 [1]. [Pg.184]

Clausius R 1857 Uber die Art von Bewegegung, die wir Warme nennen Ann. Phys. Chem. 100 353... [Pg.210]

Equation (A2.1.21) includes, as a special case, the statement dS > 0 for adiabatic processes (for which Dq = 0) and, a fortiori, the same statement about processes that may occur in an isolated system (Dq = T)w = 0). If the universe is an isolated system (an assumption that, however plausible, is not yet subject to experimental verification), the first and second laws lead to the famous statement of Clausius The energy of the universe is constant the entropy of the universe tends always toward a maximum. ... [Pg.341]

Equation (A2.1.53) is frequently called the Clausius-Clapeyronequation, although this name is sometimes applied to equation (A2.1.52). Apparently Clapeyron first proposed equation (A2.1.52) in 1834, but it was derived properly from thennodynamics decades later by Clausius, who also obtained tlie approximate equation (A2.1.53).)... [Pg.354]

This completes the heuristic derivation of the Boltzmann transport equation. Now we trim to Boltzmaim s argument that his equation implies the Clausius fonn of the second law of thennodynamics, namely, that the entropy of an isolated system will increase as the result of any irreversible process taking place in the system. This result is referred to as Boltzmann s H-theorem. [Pg.683]

If we consider the optical response of a molecular monolayer of increasing surface density, the fomi of equation B 1.5.43 is justified in the limit of relatively low density where local-field interactions between the adsorbed species may be neglected. It is difficult to produce any rule for the range of validity of this approximation, as it depends strongly on the system under study, as well as on the desired level of accuracy for the measurement. The relevant corrections, which may be viewed as analogous to the Clausius-Mossotti corrections in linear optics, have been the... [Pg.1288]

In this case, the scattering serves as a means for counting the number of molecules (or particles, or objects) per unit volume (N/V). It is seen that the polarizability, a, will be greater for larger molecules, which will scatter more. If we take the Clausius-Mosotti equation [16] ... [Pg.1389]

The pressure is usually calculated in a computer simulation via the virial theorem ol Clausius. The virial is defined as the expectation value of the sum of the products of the coordinates of the particles and the forces acting on them. This is usually written iV = X] Pxi where x, is a coordinate (e.g. the x ox y coordinate of an atom) and p. is the first derivative of the momentum along that coordinate pi is the force, by Newton s second law). The virial theorem states that the virial is equal to —3Nk T. [Pg.323]

Another way to obtain a relative permitivity is using some simple equations that relate relative permitivity to the molecular dipole moment. These are derived from statistical mechanics. Two of the more well-known equations are the Clausius-Mossotti equation and the Kirkwood equation. These and others are discussed in the review articles referenced at the end of this chapter. The com-... [Pg.112]

Numerous mathematical formulas relating the temperature and pressure of the gas phase in equilibrium with the condensed phase have been proposed. The Antoine equation (Eq. 1) gives good correlation with experimental values. Equation 2 is simpler and is often suitable over restricted temperature ranges. In these equations, and the derived differential coefficients for use in the Hag-genmacher and Clausius-Clapeyron equations, the p term is the vapor pressure of the compound in pounds per square inch (psi), the t term is the temperature in degrees Celsius, and the T term is the absolute temperature in kelvins (r°C -I- 273.15). [Pg.389]

Substitution of V = RT/P into the foregoing equation and rearranging gives the Clausius-Cla-peyron equation. [Pg.534]

This result, called the Clausius-Mosotti equation, gives the relationship between the relative dielectric constant of a substance and its polarizability, and thus enables us to express the latter in terms of measurable quantities. The following additional comments will connect these ideas with the electric field associated with electromagnetic radiation ... [Pg.668]

The Clausius-Mosotti equation with n written for can be used to... [Pg.678]

The Clausius-Mosotti equation relates the polarizability of a substance to... [Pg.680]

Vapor Pressures and Adsorption Isotherms. The key variables affecting the rate of destmction of soHd wastes are temperature, time, and gas—sohd contacting. The effect of temperature on hydrocarbon vaporization rates is readily understood in terms of its effect on Hquid and adsorbed hydrocarbon vapor pressures. For Hquids, the Clausius-Clapeyron equation yields... [Pg.47]

The vapor pressure for the soHd at 25°C has been calculated from the value for the Hquid at 70°C and the heats of vaporization and fusion using the Clausius-Clapeyron relationship. [Pg.428]

Fundamental Property Relation. The fundamental property relation, which embodies the first and second laws of thermodynamics, can be expressed as a semiempifical equation containing physical parameters and one or more constants of integration. AH of these may be adjusted to fit experimental data. The Clausius-Clapeyron equation is an example of this type of relation (1—3). [Pg.232]

If the latent heat of vaporization is then assumed to be constant over the temperature range of interest, equation 6 can be integrated to give the Clausius-Clapeyron expression ... [Pg.233]

Two empirical parameters are evident in equation 7, the heat of vaporization and the integration constant, I. Experimental data indicate that the linear relationship suggested by Clausius-Clapeyron may not be followed over a large temperature range (4) therefore additional adjustable parameters have been added to equation 7 to improve its correlating abiUty. The most prominent of these is the Antoine equation ... [Pg.233]

Reference Substances. Use of a reference substance has its origins in the work of Clausius-Clapeyron and equation 73, a form of equation 7 ... [Pg.242]

Curve fitting to data is most successhil when the form of the equation used is based on a known theoretical relationship between the variables associated with the data points, eg, use of the Clausius-Clapeyron equation for vapor pressure. In the absence of known theoretical relationships, polynomials are one of the most usehil forms to describe a curve. Polynomials are easy to evaluate the coefficients are linear and the degree, ie, the highest power appearing in the equation, is a convenient measure of smoothness. Lower orders yield smoother fits. [Pg.245]

Enthalpy of Vaporization The enthalpy (heat) of vaporization AHv is defined as the difference of the enthalpies of a unit mole or mass of a saturated vapor and saturated liqmd of a pure component i.e., at a temperature (below the critical temperature) anci corresponding vapor pressure. AHy is related to vapor pressure by the thermodynamically exact Clausius-Clapeyron equation ... [Pg.393]

As an example of how the approximate thermodynamic-property equations are handled in the inner loop, consider the calculation of K values. The approximate models for nearly ideal hquid solutions are the following empirical Clausius-Clapeyron form of the K value in terms of a base or reference component, b, and the definition of the relative volatility, Ot. [Pg.1288]

Isosteric Heat of Adsorption The most useful heat of adsorption for fixed-bed calculations is the Isosteric heat of adsorption, which is given by the Clausius-Clapeyron type relation... [Pg.1504]

Nomograph defined. This method assumes the application of the Clausius-Clapeyron equation, Henry s law, and... [Pg.366]

Better examples of shortcut design methods developed from property data are fractionator tray efficiency, from viscosity " and the Clausius-Clapeyron equation which is useful for approximating vapor pressure at a given temperature if the vapor pressure at a different temperature is known. The reference states that all vapor pressure equations can be traced back to this one. [Pg.402]

Unfortunately values of A// at sueh low temperatures are not readily available and they have to be eomputed by means of the Clausius-Clapeyron equation or from the equation given by Hildebrand and Scott" ... [Pg.90]

Pq the dipole or orientation polarisation P itself is defined by the Clausius-Mosotti Equation... [Pg.117]


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Adsorption Clausius-Clapeyron equation

Boiling point elevation Clausius-Clapeyron equation

Carnots Theorem and the Entropy of Clausius

Characteristic temperature Clausius

Chemical equations Clausius-Clapeyron equation

Chemical potential Clausius

Chemical potential Clausius-Clapeyron equation

Claperyon-Clausius equation

Clausius - Clapeyron equation generalized

Clausius Clapeyron law

Clausius Clapyron equation

Clausius Formulation of the Second Law

Clausius Gibbs

Clausius Mossotti field

Clausius Statements in Detail

Clausius Thermodynamics

Clausius analysis

Clausius equality

Clausius equation of state

Clausius equation, phase diagrams

Clausius equations

Clausius external fields

Clausius generalized

Clausius inequality

Clausius inequality and the change of entropy for nonequilibrium processes

Clausius inequality entropy change

Clausius principle

Clausius s formula

Clausius spontaneous change

Clausius statement

Clausius statement of the second law

Clausius theorem

Clausius* postulate

Clausius, Rudolf

Clausius, Rudolf Julius Emanuel

Clausius, Rudolf Julius Emmanuel

Clausius, Rudolph

Clausius, virial theorem

Clausius-CIapeyron equation

Clausius-Claperyron Equation

Clausius-Clapeyron

Clausius-Clapeyron equation

Clausius-Clapeyron equation Closed system

Clausius-Clapeyron equation and

Clausius-Clapeyron equation changes

Clausius-Clapeyron equation derivation

Clausius-Clapeyron equation integrated form

Clausius-Clapeyron equation integration

Clausius-Clapeyron equation metal

Clausius-Clapeyron equation pure solid-vapor equilibrium

Clausius-Clapeyron equation, application

Clausius-Clapeyron equation, enthalpy

Clausius-Clapeyron equation, enthalpy vaporization

Clausius-Clapeyron equation, equilibrium phase

Clausius-Clapeyron equation: use

Clausius-Clapeyron plot

Clausius-Clapeyron relation

Clausius-Clapeyron relationship

Clausius-Clapyeron equation

Clausius-Duhem inequality

Clausius-Mosotti

Clausius-Mosotti equation

Clausius-Mosotti expression

Clausius-Mosotti model

Clausius-Mosotti relationship

Clausius-Mosotti theory

Clausius-Mosotti-Debye equation

Clausius-Mosotti-Lorentz equation

Clausius-Mosotti: relation

Clausius-Mossoti formula

Clausius-Mossoti function

Clausius-Mossotti

Clausius-Mossotti equation

Clausius-Mossotti factor

Clausius-Mossotti formula

Clausius-Mossotti function

Clausius-Mossotti local field

Clausius-Mossotti relation

Clausius-Mossotti relationship

Clausius-Mossotti theory

Clausius-Mossotti, continuum

Clausius-Mossotti/Lorentz-Lorenz

Clausius-Mossotti/Lorentz-Lorenz model

Clausius—Mosotti and Debye Equations

Clausius’ virial

Electric Clausius-Mossotti

Energy Clausius

Equation Carnot-Clausius

Equation of Clausius-Clapeyron

Equation, Arrhenius Clausius-Clapeyron

Equations, mathematical Clausius-Clapeyron

Equilibria Clausius-Clapeyron equation

Formulation of Clausius

Gas and condensed phase equilibrium the Clausius-Clapeyron equation

Gases Clausius-Clapeyron equation

Heat Clausius-Clapeyron equation

Inequality of Clausius

Integration of the Clausius-Clapeyron equation

Irreversible processes, Clausius

Liquids Clausius-Clapeyron equation

Molar volume Clausius-Clapeyron equation

Phase Clausius-Clapeyron equation

Phase transitions Clausius-Clapeyron equation

Plank - Clausius Equation

Pressure Clausius-Clapeyron equation

Second law Clausius

Single-component systems Clausius-Clapeyron equation

Solids Clausius-Clapeyron equation

Table Clausius-Clapeyron equations

The Clausius Equation

The Clausius and Kirchhoff equations

The Clausius inequality

The Clausius-Clapeyron Equation

The Clausius-Clapeyron Equation and Hydrate Equilibrium

The Clausius-Mosotti equation

The Clausius-Mosotti relation

The Kelvin and Clausius Formulations

The Postulates of Kelvin and Clausius

The Second Law and Clausius

The assumptions of Clausius

Theoretical Limits on Perpetual Motion Kelvins and Clausius Principles

Thermodynamics Clausius statement

Thermodynamics Clausius-Clapeyron equation

Uncompensated heat, Clausius

Vapor pressure Clausius-Clapeyron Equation

Vaporization Clausius-Clapeyron equation

Virial theorem of Clausius

Volume Clausius-Clapeyron equation

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