Internal energy entropy coefficient

In this paper, general expressions for internal energy, entropy, enthalpy, etc., are presented in terms of the strain energy function and its temperature coefficient. 

Equation (3.16) shows that the force required to stretch a sample can be broken into two contributions one that measures how the enthalpy of the sample changes with elongation and one which measures the same effect on entropy. The pressure of a system also reflects two parallel contributions, except that the coefficients are associated with volume changes. It will help to pursue the analogy with a gas a bit further. The internal energy of an ideal gas is independent of volume The molecules are noninteracting so it makes no difference how far apart they are. Therefore, for an ideal gas (3U/3V)j = 0 and the thermodynamic equation of state becomes... 

Equations (4-41) and (4-42) are general expressions for the internal energy and entropy of homogeneous fluids at con stant composition as functions of temperature and molar vohime. The coefficients of dT and dv are expressed in terms of measurable quantities. 

These expressions demonstrate that the change of entropy and internal energy on deformation under these conditions is both intra- and intermolecular in origin. Intramolecular (conformational) changes, which are independent of deformation, are characterized by the temperature coefficient of the unperturbed dimensions of chains d In intermolecular changes are characterized by the thermal expansivity a and are strongly dependent on deformation. The difference between the thermodynamic values under P, T = const, and V, T = const, is vefy important at small deformations since at X - 1 2aT/(/,2 + X — 2) tends to infinity. 

Extended nonequilibrium thermodynamics is not based on the local equilibrium hypothesis, and uses the conserved variables and nonconserved dissipative fluxes as the independent variables to establish evolution equations for the dissipative fluxes satisfying the second law of thermodynamics. For conservation laws in hydrodynamic systems, the independent variables are the mass density, p, velocity, v, and specific internal energy, u, while the nonconserved variables are the heat flux, shear and bulk viscous pressure, diffusion flux, and electrical flux. For the generalized entropy with the properties of additivity and convex function considered, extended nonequilibrium thermodynamics formulations provide a more complete formulation of transport and rate processes beyond local equilibrium. The formulations can relate microscopic phenomena to a macroscopic thermodynamic interpretation by deriving the generalized transport laws expressed in terms of the generalized frequency and wave-vector-dependent transport coefficients. 

Free Energy (kcal/mol) Internal Energy (kcal/mol) Entropy (cal-mol deg ) Pressure (atm) Thermal Pressure Coefficient (atm/deg) Heat Capacity (cal-mol deg" )... 

P = absolute pressure T — absolute temperature V = specific volume p = density = 1/F S = specific entropy H = specific enthalpy U = specific internal energy Cp — specific heat capacity at constarit pressure C = specific heat capacity at constant volume C(T = specific heat capacity at constant saturation W = velocity of sound fx = Joule-Thomson coefficient R = universal gas constant... 

W. M. Haynes and R. D. Goodwin, Thermophysical Properties of Normal Butane from 135 to 700 K at Pressures to 70 MPa, U.S. Dept, of Commerce, National Bureau of Standards Monograph 169, 1982, 192 pp. Tabulated data include densities, compressibility factors, internal energies, enthalpies, entropies, heat capacities, fugacities and more. Equations are given for calculating vapor pressures, liquid and vapor densities, ideal gas properties, second virial coefficients, heats of vaporization, liquid specific heats, enthalpies and entropies. 

In order to understand the meaning of the different transport coefficients arising in the liquid vapour phase change we consider a liquid surface at temperature T with an adjacent vapour phase at temperature T (Fig.l). The vapour pressure is assumed to be so low that gas collisions can be neglected (Knudsen gas). The entropy flux can be expressed in terms of the flux of internal energy and the mass flux J by the following equation... 

This book presents the results of a reassessment and correlation of the thermodynamic data for water. It supersedes the Keenan and Keyes Tables of 1936. Values are tabulated for the specific volume, Internal energy, and enthalpy, as functions of temperature and pressure. Also given are data for vapor-liquid and vapor-solid equilibrium, superheated vapor, and the compressed liquid. Mollier and temperature-entropy charts are included along with charts of heat capacity of liquid and vapor, Prandtl number, and isentropic expansion coefficient. The data and tables are discussed in an appendix of 25 pages and a list of 37 references is given. Also see items [43] and [134] for other correlations. 

Now we aim to calculate the thermodynamic functions and the thermodynamic coefficients knowing the canonical partition function of the system. We will begin with the internal energy and the entropy, and then once these two functions are known, the other thermodynamic functions or their derivatives can easily be calculated. 

With the expressions of internal energy and entropy, we can calculate all other thermodynamic functions defined by them. This is the same for the primary and secondary partial derivatives of these thermodynamic functions, i.e. the conjugate variables of the problem variables including pressure (or its opposite), entropy, the chemical potential and the thermodynamic coefficients which are the secondary derivatives of thermodynamic functions. Below are the results, easily obtained for any of the variables. 

NIST/ASME Steam Properties Database versiou 2.21 http //www.nist.gov/srd/nistlO.cfm (accessed November 10, 2010) (purchase required). Thermophysical properties include in the STEAM Database temperature, Helmholtz energy, thermodynamic derivatives, pressure, Gibbs energy, density, fugacity, thermal conductivity, volume, isothermal compressibility, viscosity, dielectric constant, enthalpy, volume expansivity, dielectric derivatives, internal energy, speed of sound, Debye-Hlickel slopes, entropy, Joule-Thomson coefficient, refractive index, heat capacity, surface tension. The STEAM database generates tables and plots of property values. Vapor-liquid-solid saturation calculations with either temperature or pressure specified are available. 

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