Volume compressibility, isothermic

Figure 4.2. Pressure-volume compression curves. For isentrope and isotherm, the thermodynamic path coincides with the locus of states, whereas for shock, the thermodynamic path is a straight line to point Pj, V, on the Hugoniot curve, which is the locus of shock states.

Sf.I f-Tfst 4.4B In a petroleum refinery a 750.-L container containing ethylene gas at 1.00 bar was compressed isothermally to 5.00 bar. What was the final volume of the container ... 

Self-Test 4.8B A sample of dry air in the cylinder of a test engine at 80. cm3 and 1.00 atm is compressed isothermally to 3.20 atm by pushing a piston into the cylinder. What is the final volume of. the sample ... 

Self-Test 6.6A Suppose that 2.00 mol C02 at 2.00 atm and 300. K is compressed isothermally and reversibly to half its original volume before being used to produce soda water. Calculate w, q, and AU by treating the C02 as an ideal gas. 

Self-Test 7.3A Calculate the change in molar entropy of an ideal gas when it is compressed isothermally to one-third its initial volume. 

The remaining N — x molecules are compressed isothermally and reversibly from original volume V — xvl to a final volume V — givL. Thus the total volume remains constant. This work is approximately... 

Energies, Excess Enthalpies, Excess Volumes, and Isothermal Compressibilities of Cyclohexane + 2,3-Dimethylbutane , J. Client. Thermodyn., 6, 35-41 (1974). J. B. Ott, K. N. Marsh, and R. H. Stokes, Excess Enthalpies, Excess Gibbs Free Energies, and Excess Volumes for (Cyclohexane + n-Hexane), and Excess Gibbs Free Energies and Excess Volumes for (Cyclohexane + Methylcyclohexane) at 298.15 and 308.15 K , J. Chem. Thermodyn., 12, 1139-1148 (1980). 

One mole of an ideal gas, initially at 20°C and 1 bar, undergoes the following mechanically reversible changes. It is compressed isothermally to a point such that when it is heated at constant volume to 100 0 its final pressure is lObar. Calculate Q, W, AU, and AH for the process. Take... 

A particular quantity of an ideal gas [Cv = (5/2) R] undergoes the following mechanically reversible steps that together form a cycle. The gas, initially at 1 bar and 300 K, is compressed isothermally to 3 bar. It is then heated at constant P to a temperature of 900 K. Finally, it is cooled at constant volume to its initial state with the extraction of 1,300 J as heat. Determine Q and IV for each step of the cycle and for the complete cycle. 

Clausius/Clapeyron equation, 182 Coefficient of performance, 275-279, 282-283 Combustion, standard heat of, 123 Compressibility, isothermal, 58-59, 171-172 Compressibility factor, 62-63, 176 generalized correlations for, 85-96 for mixtures, 471-472, 476-477 Compression, in flow processes, 234-241 Conservation of energy, 12-17, 212-217 (See also First law of thermodynamics) Consistency, of VLE data, 355-357 Continuity equation, 211 Control volume, 210-211, 548-550 Conversion factors, table of, 570 Corresponding states correlations, 87-92, 189-199, 334-343 theorem of, 86... 

B A system consists of 5 kg of water vapor at the dew point. The system is compressed isothermally at 400K, and 400kJ of work are done on the system by the surroundings. What volume of liquid was present in the system before and after compression ... 

C Solid carbon dioxide (dry ice) has innumerable uses in industry and in research. Because it is easy to manufacture, the competition is severe, and it is necessary to make dry ice very cheaply to be successful in selling it. In a proposed plant to make dry ice, the gaseous CO2 is compressed isothermally and essentially reversibly from 6 psia and 40°F to a specific volume of 0.05 ft3/lbm. 

The P-V Isotherms of Carbon Dioxide The importance of critical temperature of a gas was first discovered by T. Andrews in his experiments on pressure-volume relationships (isotherms) of carbon dioxide gas at a series of temperatures. The isotherms of carbon dioxide determined by him at different temperatures is shown in the figure given above. Consider first the isothermal at the lowest temperature, viz., 13.1 C. The point A represents carbon dioxide in gaseous state occupying a certain volume under a certain pressure. On increasing the pressure, its volume diminishes as is indicated by the curve AB. At B which represents a pressure of 49.8 atm, liquefaction of the gas commences and thereafter a rapid decrease in volume takes place at the same pressure, as more and more of the gas is converted into the liquid state. At C, the gas has been completely liquefied. Now, as the liquid is only slightly compressible, further increase of pressure produces only a very small decrease in volume. A steep line CD that is almost vertical shows this. 

Therefore, it is important to have a theoretical tool which allows one to examine (or even predict) the thickness of the LC region and the value of the LC on the basis of more easily available experimental information regarding liquid mixtures. A powerful and most promising method for this purpose is the fluctuation theory of Kirkwood and Buff (KB). " The KB theory of solutions allows one to extract information about the excess (or deficit) number of molecules, of the same or different kind, around a given molecule, from macroscopic thermodynamic properties, such as the composition dependence of the activity coefficients, molar volume, partial molar volumes and isothermal compressibilities. This theory was developed for both binary and multicomponent solutions and is applicable to any conditions including the critical and supercritical mixtures. 

Kirkwood and Buff [15] obtained expressions for those quantities in compact matrix forms. For binary mixtures, Kirkwood and Buff provided the results listed in Appendix A. Starting from the matrix form and employing the algebraic software Mathematica [16], analytical expressions for the partial molar volumes, the isothermal compressibility and the derivatives of the chemical potentials for ternary mixtures were obtained by us. They are listed in Appendix B together with the expressions at infinite dilution for the partial molar volumes and isothermal compressibility. 

For binary mixtures, Kirkwood and Buff [15] obtained the following expressions for the partial molar volumes, the isothermal compressibility and the derivatives of the chemical potentials with respect to concentrations. 

It was shown previously [5,14] that the KB theory of solution can be used to relate the thermodynamic properties of ternary mixtures, such as the partial molar volumes, the isothermal compressibility and the derivatives of the chemical potentials to the KB integrals. In particular for the derivatives of the activity coefficients one can write the following rigorous relations [5] ... 

Isothermal volume compressibilities -yVidV/dP) are 6.9 X 10"2.7 x 10 , and 0.18 x 10 cm /dyne for solid Cfto, graphite, and diamond, respectively. Clearly, fiillerite is the softest all-C solid currently known. The linear compressibility normal to the close-packed planes is nearly equal for solid C o and graphite (11). This suggests that there should be no elastic impediments to the formation of intercalated (12) fullerites. 

COMPRESSION/EXPANSION OF AN IDEAL GAS Consider an ideal gas enclosed in a piston-cylinder arrangement that is maintained at constant temperature in a heat bath. The gas can be compressed (or expanded) reversibly by changing the position of the piston to accomplish a specified change in volume. In Section 12.6, the heat transferred between system and bath when the gas is expanded (or compressed) isothermally and reversibly from volume Vi to Vi is shown to be... 

The cyhnder efficiency of an air compressor may be defined as the ratio of the work done in a complete cycle to compress isothermally a volume of air at atmospheric pressure equal to the intake piston displacement, divided by the actual work done in the air cyhnder. This would be the area AKCG (Fig. 30) divided by the shaded area or the actual work done in the air cylinder. 

The efficiency of compression may be defined as the product of the cylinder efficiency and the true volumetric efficiency, or it is the work done in a complete cycle to compress isothermally (without clearance) a given volume of free air, divided by the work actually expended in compressing the same volume of free air. 

In 2002, Morrow and Maginn presented an all-atom force field for [C4mim][PF6] using a combination of DFT calculations (B3LYP/6-311+G ) and CHARMM 22 parameter values [13]. MD simulations were carried out in the isothermal-isobaric ensemble at three different temperatures. The calculated properties contained infrared frequencies, molar volumes, volume expansivities, isothermal compressibilities, self-diffusivities, cation-anion exchange rates, rotational dynamics, and radial distribution functions. These thermodynamic properties were found to be in good agreement with available experimental values [13]. 

III. The nonconducting jacket is now removed and the cylinder is placed in the heat reservoir at Tx- The gas is compressed isothermally and reversibly, the external pressure being maintained infinitesimally greater than the gas pressure, and the temperature of the gas infinitesimally greater than that of the reservoir. The process is represented by the isothermal path CD in Fig. 11, the final volume being Vd. The work done is given by... 

The exit Mach number for compressible isothermal fluid has been shown to be M 1, but l/v/k, where k is the ratio of the fluid specific heat capacities at constant pressure to that at constant volume. Table 3-5 shows the k values for some common gases. The following cases are such ... 

Calculation of Compressed Liquid Excess Volumes and Isothermal Compressibilities for Mixtures of Simple Species... 

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