Isochoric heating

A more recent compilation includes tables giving temperature and PV as a function of entropies from 0.573 to 0.973 (2ero entropy at 0°C, 101 kPa (1 atm) and pressures from 5 to 140 MPa (50—1400 atm) (15). Joule-Thorns on coefficients, heat capacity differences (C —C ), and isochoric heat capacities (C) are given for temperatures from 373 to 1273 K at pressures from 5 to 140 MPa. 

In the Kieffer model (Kieflfer 1979a, b, and c cf section 3.3), the isochoric heat capacity is given by... 

The isochoric heating process of a Lenoir engine receives air at 15°C and 101 kPa. The air is heated to 2000° C, and the mass of air contained in the cylinder is 0.01kg. Determine the pressure at the end of the isochoric heating process, the temperature at the end of the isentropic expansion process, heat added, heat removed, work added, work... 

A second, less cumbersome, phase in the detn of temp of expln involves the calcn of both the isochoric heat of expln, Hgf O gas) of the explosive and the internal energies of the expln products at temp T relative to ambient temp ft It is shown in this rept that the... 

Equation (11.163) shows how the isochoric heat capacity of a heterogeneous two-phase system can be evaluated from known isobaric properties (CP, aP) of the individual phases and the direction y(T of the coexistence coordinate cr. 

While there are conflicting views about the performances and benefits of all these versions, there are some criteria that may serve for a critical assessment. These include (a) Onsager s well-known lower bound for the mean electrostatic energy per ion [253] in its reformulation by Totsuji [254] and (b) Gillan s upper bound for the free energy [255]. Moreover, the condition for thermal stability requires the configurational isochoric heat capacity to be positive. 

Isochoric heat capacity of crystals can be presented as a sum of contributions from lattice vibrations (6 degrees of freedom) and intramolecular vibrations (3n-6 degrees of freedom, where n is a number of atoms in a molecule)... 

Recent developments in ultrashort, high-peak-power laser systems, based on the chirped pulse amplification (CPA) technique, have opened up a new regime of laser-matter interactions [1,2]. The application of such laser pulses can currently yield laser peak intensities well above 1020 W cm 2 at high repetition rates [3]. One of the important features of such interactions is that the duration of the laser pulse is much shorter than the typical time scale of hydrodynamic plasma expansion, which allows isochoric heating of matter, i.e., the generation of hot plasmas at near-solid density [4], The heated region remains in this dense state for 1-2 ps before significant expansion occurs. 

What Gucker and Rubin called the apparent molal isochoric heat capacity of an electrolyte is (P(Co2), and the corresponding isopiestic heat capacity is 0(Cp2), where ... 

Gases Methods for estimating low-pressure gas thermal conductivities are based on kinetic theory and generally correlate the dimensionless group kM/r C (M = molecular weight, T] = viscosity, C = isochoric heat capacity) known as the Eucken factor. The method of Stiel and Thodos is recommended for pure nonpolar compounds, and the method of Chung is recommended for pure polar compounds. 

Table 1 Rate-controlled sequences of heating and cooling chosen for T h and T measurements. First, heating along the liquid-vapour curve (diphasic inclusion), then isochoric heating followed by isochoric cooling down (single-phase inclusion).

Figure 1. Coexistence curve with isochores and the isochoric slope, j/0. At points A and B the curvature of the isochores is zero as well as along the locus indicated by the dotted line (the locus of the isochoric heat...

Helmholtz energy Gibbs energy Isobaric heat capacity Isochoric heat capacity Isobaric expansivity Isothermal compressibility Isentropic compressibility... 

These tables summarize the thermophysical properties of air in the liquid and gaseous states as calculated from the pseudo-pure fluid equation of state of Lemmon et al. (2000). The first table refers to liquid and gaseous air at equilibrium as a function of temperature. The tabulated properties are the bubble-point pressure (i.e., pressure at which boiling begins as the pressure of the liquid is lowered) the dew-point pressure (i.e., pressure at which condensation begins as the pressure of the gas is raised) density (/ ) enthalpy (H) entropy (S) isochoric heat capacity (CJ isobaric heat capacity (C ) speed of sound (u) viscosity (rj) and thermal conductivity (A). The first line of identical temperatures is the bubble-point (liquid) and the second line is the dewpoint (vapor). The normal boiling point of air, i.e., the temperature at which the bubble-point pressure reaches 1 standard atmosphere (1.01325 bar), is 78.90 K (-194.25 °C). 

These tables give thermodynamic and transport properties of a variety of fluids, as generated from the equations of state presented in the references below. The properties tabulated are pressure (P), density (p), enthalpy (H), entropy (S), isochoric heat capacity (C, isobaric heat capacity (C ), speed of sound (u), viscosity (tj), thermal conductivity (A), and static dielectric constant (D). AU extensive properties are given on a mass basis. Not all properties are included for every substance. The references should be consulted for information on the uncertainties. 

Since conformational defects generally loosen bonds, an energy level diagram of the form shown in Fig. 2.5 is expected. In the determination of the entropy s, the internal energy u and the isochoric heat capacity c, it is assumed that the interaction parameters and Au are independent of temperature. 

Cy 1+ " Isochoric heat capacity derived using Cpy the isobaric expansion coefficient, Opy and the sound velocity, c. 

Isochoric heat capacity is somewhat more complicated to calculate than Cp. As has been shown for pulse-heating experiments [42-44], Cy may be obtained if Cp, the isobaric expansion coefficient and the speed of sound of the test material are known. 

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