Isothermal changes

Neumann has adapted the pendant drop experiment (see Section II-7) to measure the surface pressure of insoluble monolayers [70]. By varying the droplet volume with a motor-driven syringe, they measure the surface pressure as a function of area in both expansion and compression. In tests with octadecanol monolayers, they found excellent agreement between axisymmetric drop shape analysis and a conventional film balance. Unlike the Wilhelmy plate and film balance, the pendant drop experiment can be readily adapted to studies in a pressure cell [70]. In studies of the rate dependence of the molecular area at collapse, Neumann and co-workers found more consistent and reproducible results with the actual area at collapse rather than that determined by conventional extrapolation to zero surface pressure [71]. The collapse pressure and shape of the pressure-area isotherm change with the compression rate [72]. 

The second step is the evaluation of the change in fugacity of the liquid with a change in pressure to a value above or below For this isothermal change of state from saturated liquid at to liquid at pressure P, Eq. (4-105) is integrated to give... 

For an isothermal change, the expression for P from the Redlich-Kwong equation can be substituted into the general formula for work done ... 

Isothermal change A process that takes place at constant temperature, such as the isothermal expansion of a gas. 

Latent heat The quantity of heat that is absorbed or released in an isothermal transformation of phase, in kj kg C b Latent heat of vaporization The heat added during an isothermal change of phase from liquid to gas. 

At large distances the curve of Fig. 8b is a plot of — (c2/ r)> where t is the macroscopic dielectric constant of the solvent at the temperature considered. For small values of r the curve deviates from this value but at every point the slope of the curve must represent the mean intensity of the mutual attraction or repulsion at the particular temperature considered. If the curve of Fig. 86 for dissociation in solution is to be useful, every point on this curve must belong to the same temperature T. That is to say, when we consider any change in the distance r between the ions, we are interested in an isothermal change in r. 

Such a fluid is an ideal gas undergoing isothermal change of volume (cf. 77). 

The magnitude on the left is the heat absorbed in the isothermal change, and of the two expressions on the right the first is dependent only on the initial and final states, and may be called the compensated heat, whilst the second depends on the path, is always negative, except in the limiting case of reversibility, and may be called the uncompensated heat. From (3) we can derive the necessary and sufficient condition of equilibrium in a system at constant temperature. 

Then, either no change at all can occur, or all possible changes are reversible. Hence, if we imagine any isothermal change in the state of the system, and calculate the value of Tco for that change, this value will be positive or zero if the former state is an equilibrium state. 

Since is essentially positive for all real changes, (7) shows that in all real isothermal changes the magnitude 4 — 4q + AT must diminish, and that in any small virtual change ... 

The equation (16) shows that the increase of bound energy in a reversible isothermal change is equal to the increase of entropy multiplied by the absolute temperature, so that the entropy may be regarded as the capacity for bound energy in such changes. B will evidently contain the arbitrary term / IT. 

For an isothermal change in an ideal gas, the product of pressure and volume is a constant. For unit mass of gas ... 

A change of state according to equation 6.27 is called a polytropic change. Two special cases are the isothermal change and the adiabatic... 

As the name implies, an isothermal change takes place at constant temperature. This requires that the process be relatively slow and heat transfer between the gas and the surroundings be rapid. An isothermal change corresponds to k = 1 and equation 6.27 becomes... 

Often the upstream pressure P will be unknown but for an isothermal change P VX can be replaced by any known value of PV at the same temperature, for example the downstream conditions P2V2 if P2 is specified. 

We can show that the enthalpy, as well as the internal energy, is constant in any isothermal change of an ideal gas as follows ... 

TABLE 5.1. Thermodynamic Quantities for Isothermal Changes in an Ideal Gas... 

Thus far we have observed that the Gibbs and Planck functions provide the criteria of spontaneity and equilibrium in isothermal changes of state at constant pressure. If we extend our analysis to systems in which other constraints are placed on the system, and therefore work other than mechanical work can be performed, we find that the Gibbs and Helmholtz functions also supply a means for calculating the maximum magnitude of work obtainable from an isothermal change. 

As we are concerned with isothermal changes, —SdT can be added to the left side of Equation (7.74) without changing its value ... 

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