Gas—Isothermal

If the fluid can be described by the ideal gas law (e.g., air, under normal atmospheric conditions), then 

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Let us define the system as being characterized by an empirical temperature,aa 9 and any other number of variables, at, aa,. .., v . Initially, we will change only two independent variables, 9 and x. Our generalized example will be set up in such a way as to be consistent with the behavior of gas isotherms. That is, 9 will behave in a way analogous to temperature T, and the other variable, at, will be the analogue of pressure p. Then, we will consider the implications when 9 and another variable are allowed to change. 

Figure 3.4 Carnot cycle for the expansion and compression of an ideal gas. Isotherms alternate with adiabats in a reversible closed path. The shaded area enclosed by the curves gives the net work in the cyclic process.

Sflf-T 1ST 6.2A A cylinder of volume 2.00 L contains 1.00 mol He(g) at 30°C. Which process does more work on the system, compressing the gas isothermally to 1.00 I. with a constant external pressure of 5.00 atm or compressing it reversibly and isothermally to the same final volume ... 

These two relations are known as Boyle s law. The law implies that if we compress a gas isothermally (at constant temperature) into half its initial volume, from 1 L to 0.5 L, or from 10 mL to 5 mL, or from any initial volume to half that volume, then the pressure of the gas will double. 

As discussed in Chapter 2, the change in entropy associated with taking 1 mol of an ideal gas isothermally from pressure Pt to a pressure P2 is given by... 

Infinite-Step Compression. Notice that in compressing the gas isothermally, as the number of steps increases, the work required to compress the gas decreases. 

It may be of interest to compare the effect of the overpotential on the work performed in, say, charging a battery with the work needed to compress a gas isothermally at a finite rate. We recall that the work required to compress a gas is ... 

Ideal adsorbed solution theory (lAST) [4] is a widely used engineering thermodynamic method, the equivalent to the Raoult s law for adsorption, which uses the pure-gas isotherms as inputs to predict the mixture adsorption equilibrium at the temperature of interest. Before the lAST calculation, the pure gas isotherm must be fitted with a suitable isotherm equation to an acceptable degree of accuracy we used a piece-wise fit [3]. 

The fugacity equations are solved using absolute variables. As discussed previously, the single-gas isotherms at sub-atmospheric pressure provide the absolute isotherm in the form fiirif). Given the temperature of the isotherms, the independent variables are P and yi in the bulk gas. For a binary mixture the fugacity equations are written ... 

Ethylene is preferentially adsorbed and the individual isotherm for ethane reaches a maximum at a pressure of 3 bar. The individual isotherms show the same behavior as the single-gas isotherms shown on Figure 3 a maximum value in the amount adsorbed followed by a steep decline to zero. 

The selectivities in Figures 3 and 4 were calculated from the single-gas isotherms using Equations (13) and (14), which are written for ideal adsorbed solutions (IAS) with activity coefficients )(=1- These equations are rigorous at the limit of low pressure. At high pressure, mixtures adsorbed in nanopores display negative... 

Homogeneous gas Isothermal U-tube in temperature-controlled batch... 

Now, assume this gas isothermally fills an enclosure made of gray surfaces. The resulting enclosure problems can be treated by replacing the gas with a transparent solid partition with negligible reflectivity. 

This idea is a consequent transfer of the three-dimensional van der Waals equation into the interfacial model developed by Cassel and Huckel (cf. Appendix 2B.1). The advantages of Frumkin s position is a more realistic consideration of the real properties of a two-dimensional surface state of the adsorption layer of soluble surfactants. This equation is comparable to a real gas isotherm. This means that the surface molecular area of the adsorbed molecules are taken into consideration. Frumkin (1925) additionally introduced, on the basis of the van der Waals equation, the intermolecular interacting force of adsorbed molecules represented by a . 

Ward WH, Holdgate GA, Isothermal titration calorimetry in drug discovery. Prog. Med. Chem. 2001 38 309-376. 

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