Ideal Gas-Filled Vessels

Inert, Ideal Gas-Filled Vessels The energy available for external work following the rapid disintegration of the vessel is calcuJated by assuming that the gas within the vessel expands adiabatically to atmospheric pressure. 

Initial Fragment Velocity for Ideal-Gas-Filled Vessels... 

The general procedure of the basic method is shown in Figure 6.20. This method is suitable for calculations of bursts of spherical and cylindrical pressure vessels which are filled with an ideal gas, placed on a flat surface, and distant from other obstacles which might interfere with the blast wave. 

In the preceding subsections, bursting vessels were assumed to be filled with ideal gases. In fact, most pressure vessels are filled with fluids whose behavior cannot be described, or even approximated, by the ideal-gas law. Furthermore, many vessels are filled with superheated liquids which may vaporize rapidly, or even explosively, when depressurized. 

Figure 6.33 can be used to calculate the initial velocity Vj for bursting pressurized vessels filled with ideal gas. The quantities to be substituted, in addition to those already defined (p, po, and V), are... 

The total energy of a vessel s contents is a measure of the strength of the explosion following rupture. For both the statistical and the theoretical models, a value for this energy must be calculated. The first equation for a vessel filled with an ideal gas was derived by Brode (1959) ... 

Isotherm measurements of methane at 298 K can be made either by a gravimetric method using a high pressure microbalance [31], or by using a volumetric method [32], Both of these methods require correction for the non-ideality of methane, but both methods result in the same isotherm for any specific adsorbent [20], The volumetric method can also be used for measurement of total storage. Here it is not necessary to differentiate between the adsorbed phase and that remaining in the gas phase in void space and macropore volume, but simply to evaluate the total amount of methane in the adsorbent filled vessel. To obtain the maximum storage capacity for the adsorbent, it would be necessary to optimally pack the vessel. 

In Nature, atoms are located at different interatomic distances depending on a kind of the forces between them either by cohesion forces or chemical bonds. The latter prevail at the distances which are smaller or equal to the sum of van der Waals radii of atoms. At such distances atoms form a molecule. By definition, the van der Waals (vdW) radii of a given atom is the half of the shortest distance that is observed in crystals between the nuclei of the same atoms. The vdW radii of atoms are listed in Table 1. At the distances beymid the sum of van der Waals radii of atoms, there exists a specific van der Waals interaction often referred to as the dispersion interaction between atoms, after Johannes Diderik van der Waals who first postulated its existence in his well-known equation of state derived in his PhD thesis in 1837 and which won him the 1910 Nobel Prize in Physics. For the first time van der Waals explained the deviations of gases from the ideal behavior. Let us consider a vessel filled by a gas of atoms. Within this vessel, the pressure exerted by a gas of atoms on its wall is lower compared to that predicted by the ideal gas law since the atoms may collide with the wall and are thus retained by the attraction they undergo from the other atoms in the bulk of the gas that results in the pressure P obeying the equation [94],... 

The magnitude of deviation from ideal gas behavior can be Illustrated by comparing the results using the ideal gas law and the van der Waals equation for 1 mol of CO2 at 50°C. For a volume of 0.0269 m , the pressure would be exactly 1 bar according to the Ideal gas equation, Eq. (3.1.1). With the data of Table 3.1.1, we obtain 0.997 bar according to the van der Waals equation [Eq. (3.1.3)]. Thus, both equations give essentially the same result for ambient pressure. But if the CO2 is then compressed isothermally so that it fills a vessel that is 100 times smaller (0.000269 m ), a pressure of 100 bar is predicted by the ideal gas equation whereas the van der Waals equation yields a pressure of only 68.4 bar to achieve the same result. 

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