Volume involving gases

Gas-Cycle Systems. In principle, any permanent gas can be used for the closed gas-cycle refrigeration system however, the prevailing gas that is used is air. In the gas-cycle system operating on the Brayton cycle, all of the heat-transfer operations involve only sensible heat of the gas. Efficiencies are low because of the large volume of gas that must be handled for a relatively small refrigera tion effect. The advantage of air is that it is safe and inexpensive. 

In many important cases of reactions involving gas, hquid, and solid phases, the solid phase is a porous catalyst. It may be in a fixed bed or it may be suspended in the fluid mixture. In general, the reaction occurs either in the liquid phase or at the liquid/solid interface. In fixed-bed reactors the particles have diameters of about 3 mm (0.12 in) and occupy about 50 percent of the vessel volume. Diameters of suspended particles are hmited to O.I to 0.2 mm (0.004 to 0.008 in) minimum by requirements of filterability and occupy I to 10 percent of the volume in stirred vessels. 

Several manual and continuous analytical techniques are used to measure SO2 in the atmosphere. The manual techniques involve two-stage sample collection and measurement. Samples are collected by bubbling a known volume of gas through a liquid collection medium. Collection efficiency is dependent on the gas-liquid contact time, bubble size, SO2 concentration, and SO2 solubility in the collection medium. The liquid medium contains chemicals which stabilize SO2 in solution by either complexation or oxidation to a more stable form. Field samples must be handled carefully to prevent losses from exposure to high temperatures. Samples are analyzed at a central laboratory by an appropriate method. 

In calculations that involve gas pressure and volume, absolute pressure or pounds per square inch absolute (psia) must be used. 

Another value sometimes involved when the gas pressure is reduced before it is used is the dew point at that lower pressure condition. A major example is the use of lOOpsig (or higher) gas reduced to 15psig for use in pneumatic instruments and controls. This dew point will be lower because the volume involved increases as the pressure is decreased. The dew point at atmospheric pressure... 

Another variation which attempts to place the test upon a semiquantitative basis involves carrying out the reaction in a Smith fermentation tube. This enables one to obtain a rough idea of the volume of gas formed, but it can be misleading unless a time limit is imposed and the skins are removed. 

If it slow, then nucleation is likely to be due solely to proximity. Model D is an example of volame nucleation idiere decomposition of a solid is involved whereas Model E is that involving gas or liquid nucleation of the solid. Note that if nucleation does not occur, the solid reacts uniformly throughout its whole volume (Model F). However, this mode is rare and the nucleation stages are more likely to occur. We wUl not dwell upon how these nucleation models were derived and will only present the results here. One is referred to Appendix I wherein one can study the mathematics used to obtain the net-result. 

For fixed time assays this most frequently involves the use of standards and a calibration graph. Some methods, e.g. the use of the molar absorbance coefficient in spectrophotometry, do not requite standards and giiNometric methods permit the calculation of molar concentration from the volume of gas (1 gram mole of gas occupies 22.4 litres at standard temperature and pressure, STP). 

At this point we may define two other quantities in terms of the variables involved in Equation (59) the total volume of gas adsorbed and the volume adsorbed at monolayer coverage, V and Vmt respectively. The total volume is obviously the sum of the volume held in each type of site Vh which is proportional to iM . 

With regards to handling data on industrial apparatus for gas-liquid mass transfer (such as packed columns, bubble columns, and stirred tanks), it is more practical to use volumetric mass transfer coefficients, such as KqU and K a, because the interfacial area a cannot be well defined and will vary with operating conditions. As noted in Section 6.7.2, the volumetric mass transfer coefficients for packed columns are defined with respect to the packed volume - that is, the sum of the volumes of gas, liquid, and packings. In contrast, volumetric mass transfer coefficients, which involve the specific gas-liquid interfacial area a (L L 5), for liquid-gas bubble systems (such as gassed stirred tanks and bubble columns) are defined with respect to the unit volume of gas-liquid mixture or of clear liquid volume, excluding the gas bubbles. In this book, we shall use a for the specific interfacial area with respect to the clear liquid volume, and a for the specific interfacial area with respect to the total volume of gas-liquid mixture. 

The third factors to control and keep constant are the gas pressure and superficial gas velocity. This probably will involve gas recirculation with either a small compressor, or through a hollow shaft or some other pumping device. As seen before, the bubble diameter, the mass transfer area, the gas hold-up, and the terminal bubble-rise velocity, all depend on the superficial velocity of the gas and the power input per unit volume. When these are kept constant, the various mass transfer resistances in the pilot plant and in the large unit will be the same, hence the global rate will be conserved. The last factor is the input power to the agitator. As required for mass transfer, the scale-up must be made on the basis of constant power input per unit volume. If turbulent conditions and geometrical similarity prevail, this rule imposes the following relationship ... 

Finally, and as important as all of the features of this method, the sample can be re-equilibrated with successive fresh volumes of gas and each successive phase analyzed. The result of these series of analyses will be to define the distribution of the particular compound or compounds involved, thereby providing a measure of another physical property of the compound involved. This amounts to a qualitative mechanism of identification of trace components as a part of the primary analysis. It also provides for an extrapolation of this accumulated data to a zero equilibration stage which would be indicative of the original concentration, even though the process of taking and transporting... 

The classical method involves admitting a known quantity of gas to the sample chamber, which is usually maintained near the condensation point of the gas. Adsorption of the gas on the surface of the solid occurs, decreasing the pressure in the chamber until the adsorbed gas is in equilibrium with the free gas phase. The volume of gas adsorbed is determined by subtracting the volume of gas required to fill the free space (dead space) at equilibrium pressure from the volume of gas admitted. The dead space is obtained by precalibration of the chamber volume or by repeating the determination with a sample of negligible adsorption. The specific surface area (S), in m2/g, is given by the following... 

Aquifers for gas storage were first used in 1946 in Kentucky (United States). They are around 80 storage facilities in aquifers in the world today, most of them in the United States, the former Soviet Union and Western Europe (France, Germany and Italy). The principle of aquifer storage is to create an artificial gas field by injecting gas into the voids of an aquifer formation (involved gas volumes are similar to depleted fields). For this reason, the following geological conditions are necessary ... 

There are circumstances where weight is an important factor (Example 3), but the calculations involving gases may be in terms of volumes of gases involved. The conversion from volumes of gas to mass is done through the numbers of moles. The methods used in these problem solutions are as in Chapter 4 except that the numbers of moles converted to mass (g, lb, etc.) must be determined from the volume, temperature, and pressure of the gases. 

Once particles are present in a volume of gas, they collide and agglomerate by different processes. The coagulation process leads to substantial changes in particle size distribution with time. Coagulation may be induced by any mechanism that involves a relative velocity between particles. Such processes include Brownian motion, shearing flow of fluid, turbulent motion, and differential particle motion associated with external force fields. The theory of particle collisions is quite complicated even if each of these mechanisms is isolated and treated separately. 

Equations (4.37) to (4.42) involve eleven variables therefore five degrees of freedom must be specified. We assume constant purity of the fresh hydrogen, yH,2 = 0.95. The control structure fixes the fresh toluene flow rate Fj = 120 kmol/h and hydro-gen/toluene ratio at reactor inlet, yt,3/yH,3 =1/5. Specifying two additional variables, for example reactor volume Vand gas recycle flow rate FR, the mass-balance equations can be solved for six unknowns F2, FB, FT, FP, X and yHP. This is left as an exercise for the reader. 

When a flammable material is burned, there will be an increase in either the volume of the gas produced (provided the pressure is constant) or the pressure in the container (provided the volume is constant). Calculate the volume of gas formed during the adiabatic combustion of 100 lb moles of gaseous propane at a constant pressure of 1 atm. Assume that the 200 percent theoretical air and the propane involved in the combustion are at 25°C and that the combustion goes to completion. 

Another instructive exercise consists in examining the free expansion of a gas, depicted in Fig. 1.8.2. The gas is initially confined to a space of volume VA, volume VB being totally evacuated. A hole of macroscopic dimensions is now opened in the diaphragm separating the two volumes the gas ultimately occupies the total volume VA + VB. What is the work involved in this process The answer is not absolutely straightforward If the system is taken with boundaries encompassing only the volume VA, complications arise because... 

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