Isochoric thermal pressure coefficient

Of course, the vapour pressure is very temperature dependent, and reaches P° = 101.325 kPa at the normal boiling point, Tb. The isochoric thermal pressure coefficient, dp/dT)v = otp/KT, can be obtained from the two quantities on the right hand side listed in Table 3.1. Except at T it does not equal the coefficient along the saturation line, (dp/dT)a, which is the normal vapour pressure curve. The latter temperature dependence is often described by means of the Antoine equation ... 

Fig. 4.12 The isochoric thermal pressure coefficient, yy, of fluid mercury versus density along the liquid-vapor coexistence curve derived from isochores of Fig. 4.10. 137...

Here (dPI8T)y is the isochoric thermal pressure coefficient that is seldom measured directly and is generally obtained by the last equality in (3.22). The magnitude of is >100 MPa, so that at ambient conditions and saturation vapor pressures, the last term, -P, in Equation 3.22 can be neglected. The isobaric expansibility, a, and isothermal compressibility, Kj, are available in Table 3.3. The differences U/Vat 25°C for the solvent listed here are shown in Table 3.8, with non-stiff solvents marked by italics font. The value of U/V-P for water is by far larger than for other structured solvents, but it diminishes with increasing temperatures [30] to become commensurate with P, of other solvents above 250°C. 

The product ofT-y T-,m) is very close to the internal pressure of solutions T,m) [142], The isochoric thermal pressure coefficients monotonically increase with m... 

Thus, by using thermodynamic relations, in the same way as in the case of volumetric and thermal properties of solntions (see Eq. (2.57)), it is possible to correlate the compressibility and thermal properties. By differentiation of the isochoric thermal pressure coefficient y T m) with regard to T, the change of isochoric heat capacity with volume at constant temperature can be evaluated. Its value for pure water and citric acid solutions increases with increasing volume because the second derivative of the pressure with respect to temperature is positive, g T m) = T d P / dT )y > 0. 

AIST can calculate the values of density, compressibility, enthalpy, entropy, isochoric and isobaric heat capacity, speed of sound, adiabatic Joule-Thomson coefficient, thermal pressure coefficient, samrated vapor pressure, enthalpy of vaporization, heat capacities on the saturation and solidification lines, viscosity and thermal conductivity. Values of properties can be determined at temperatures from the triple point up to 1500 K and pressures up to 100 MPa. The system generates the following databases with appropriate algorithms and programs for their calculation ... 

The internal pressure is due to the cohesional forces (see Section 3.4.3) between the molecules that contribute to the internal energy, 17, and is equal to zero for ideal gases. The approximate equality of internal pressure values in liquids is a good criterion for the behavior of ideal liquid solutions obeying Raoult s law. In ideal liquid solutions, the molecules of the components are under similar forces in solution as in the pure liquids, and the approximate equality of internal pressures, especially for non-polar components, is the reason for their ideal behavior. On the other hand, the repulsive thermal pressure represents the tendency of a fluid to expand. The (3P/3T)V parameter is called an isochore and can be measured directly, or it is more often computed as the ratio of the coefficient of thermal expansion, a = 1/V(3V/3T)P = (31nV/3P)p, to the coefficient of compressibility, p = - l/VOV/3P)T = — (31n V/3P)T, so that (3P/3T)V = -alp. 

The second anomaly mentioned above is density anomaly. It means that density increases upon heating or that the thermal expansion coefficient becomes negative. Using the thermodynamic relation dP/dT)y = apjKr, where /> is a thermal expansion coefficient and Kp is the isothermal compressibUily and taking into account that Kj is always positive and finite for systems in equilibrium not at a critical point, we conclude that density anomaly corresponds to minimum of the pressure dependence on temperature along isochors. This is the most convenient indicator of density anomaly in computer simulation. 

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