Gases container walls

The conecting term in the pressure reflects the diminution in tire impact velocity of atoms at the containing walls of tire gas due to the attraction of the internal mass of gas, and the volume term reflects the finite volume of the molecules. Data for these two constants are shown in Table 3.4. 

Pressure is defined as force per unit area. You are probably familiar with the English unit pounds per square inch, often abbreviated psL When we say that a gas exerts a pressure of 15 psi, we mean that the pressure on the walls of the gas container is 15 pounds (of force) per square inch of wall area. 

In the kinetic theory, the gas molecules are represented by hard spheres colliding elastically with each other and with the container walls. Details of this theory are given, for example, in ref. [1], An important parameter that can be calculated by this model is A, the mean free path of a molecule between collisions. The mean free path A of molecules is ... 

Just like the walls in a squash court, against which squash balls continually bounce, the walls of the gas container experience a force each time a gas particle collides with them. From Newton s laws of motion, the force acting on the wall due to this incessant collision of gas particles is equal and opposite to the force applied to it. If it were not so, then the gas particles would not bounce following a collision, but instead would go through the wall. 

We see how each collision between a gas particle and the internal walls of the container causes the same result as if we had applied a force to it. If we call the area of the container wall A and give the symbol F to the sum of the forces of all the particles in the gas, then the pressure p exerted by the gas-particle collisions is given by... 

In summary, the pressure caused by a container housing a gas is simply a manifestation of the particles moving fast and colliding with the container walls. 

Pressure increases with increasing temperature because the collisions between the gas particles and the container wall are more energetic and occur more frequently. 

The gas particles are in constant motion, moving in straight lines in a random fashion and colliding with each other and the inside walls of the container. These collisions with the inside container walls comprise the pressure of the gas. 

The attraction of the gas particles for each other tends to lessen the pressure of the gas since the attraction slightly reduces the force of the collisions of the gas particles with the container walls. The amount of attraction depends on the concentration of gas particles and the magnitude of the intermolecular force of the particles. The greater the intermolecular forces of the gas, the higher the attraction is, and the less the real pressure. Van der Waals compensated for the attractive force by the term P + an2/V2, where a is a constant for individual gases. The greater the attractive force between the molecules, the larger the value of a. 

Equation (5-14) is combined with Bernoulli s equation. Assuming flow on a horizontal axis and using a coefficient of discharge to account for friction at the orifice, the mass flow rate of an ideal gas through a thin hole in the containment wall is ... 

Air at room temperature and pressure consists of 99.9% void and 0.1% molecules of nitrogen and oxygen. In such a dilute gas, each individual molecule is free to travel at great speed without interference, except during brief moments when it undertakes a collision with another molecule or with the container walls. The intermolecular attractive and repulsive forces are assumed in the hard sphere model to be zero when two molecules are not in contact, but they rise to infinite repulsion upon contact. This model is applicable when the gas density is low, encountered at low pressure and high temperature. This model predicts that, even at very low temperature and high pressure, the ideal gas does not condense into a liquid and eventually a solid. 

Example 2-8 Suppose the room you are in now actually contains 9.5% CH4. [You could not detect the presence of CH4 in air unless the natural gas contained a mercaptan odorizer.] If someone turned on the light switch and created a spark, what would be the temperature and pressure in the room before the windows and walls burst ... 

In the molecular flow range, on the other hand, impact of the particles with the walls predominates. As a result of reflection (but also of desorption follovi/ing a certain residence period on the container walls) a gas particle can move in any arbitrary direction in a high vacuum it is no longer possible to speak of flow in the macroscopic sense. 

In the high and ultrahigh vacuum ranges the properties of the vacuum container wall will be of decisive importance since below 10 mbar there will be more gas molecules on the surfaces than in the chamber itself. If one assumes a monomolecular adsorbed layer on the inside wall of an evacuated sphere with 1 I volume, then the ratio of the number of adsorbed particles to the number of free molecules in the space will be as follows ... 

Whenever It Is not possible to achieve the desired ultimate pressure In an apparatus there are usually two causes which can be cited The presence of leaks and/or gas being liberated from the container walls and sealants. 

In practice, container walls are usually present, and the liquid is rarely free from dust particles, adsorbed gas, absorbed gas, and foreign ions. Heterogeneous nucleation refers to the formation of nuclei on a foreign object. 

The pressure exerted on the walls is seen to depend on v2, which is proportional to the translational energy of the molecule (i.e., the kinetic energy), k.e. — 1 /2mv2. Therefore a gas containing N molecules with a distribution of x velocities will exert a pressure... 

The one-dimensional velocity distribution function will be used in Section 10.1.2 to calculate the frequency of collisions between gas molecules and a container wall. This collision frequency is important, for example, in determining heterogeneous reaction rates, discussed in Chapter 11. It is derived via a change of variables, as above. Equating the translational energy expression 8.9 with the kinetic energy, we have... 

Impingement js probably the ipost widely used principle for tiny particles collection in liquid and gas separation. This type separation depends upon entrained particles striking an obstruction rather than the containing walls. The obstructions act as collecting surfaces. 

A cone bottom (sometimes provided with sand jets) may be used to help solids pass through vertical vessels. The cone is normally at an angle to the horizontal of between 45° and 60°. Produced sand may have a tendency to stick to steel at 45°. If a cone is installed, it may be part of the pressure containing walls of the vessel, or for structural reasons, it could be installed internal to the vessel cylinder. In such a case, a gas equalizing line must be installed to assure that the vapor behind the cone is always in pressure equilibrium with the vapor space. 

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