Gases molecular speeds

Schematic view of the effect of increasing the temperature of a gas. Molecular speeds increase, resulting in more wall collisions and more force per collision, so the pressure increases.

Sensitivity to process gas molecular weight Figure 7-13d shows that TTE is not sensitive to changes in the molecular weight of the process gas. Constant speed machines show the same results. 

Maxwell distribution A relation describing the way in which molecular speeds or energies are shared among gas molecules, 121... 

The distribution of molecular speeds in gas can be determined experimentally. To du so, the gas is heated to the required temperature in an oven. The molecules then stream out of the oven through a small hole into an evacuated region. To ensure that the molecules form a narrow Iteam, they may also pass through a senes of slits, and the pressure must Ik kept very low so that collisions within the beam do not cause spreading. 

This important result is used to find the root mean square speeds of the gas-phase molecules at any temperature (Fig. 4.25). We can rewrite this equation to emphasize that, for a gas, the temperature is a measure of mean molecular speed. From... 

A plot of the Maxwell distribution for the same gas at several different temperatures shows that the average speed increases as the temperature is raised (Fig 4.27). We knew that already (Section 4.9) but the curves also show that the spread of speeds widens as the temperature increases. At low temperatures, most molecules of a gas have speeds close to the average speed. At high temperatures, a high proportion have speeds widely different from their average speed. Because the kinetic energy of a molecule in a gas is proportional to the square of its speed, the distribution of molecular kinetic energies follows the same trends. 

Maxwell distribution of molecular speeds The formula for calculating the percentage of molecules that move at any given speed in a gas at a specified temperature. 

How fast do gas molecules move Molecular speeds can be measured using a molecular beam apparatus, shown schematically in Figure 5-la. Gas molecules escape from an oven through a small hole into a chamber in which the molecular density is very low. A set of slits blocks the passage of all molecules except those moving in the... 

Molecular speed affects pressure in two ways that are illustrated in Figure 5-12. First, faster-moving molecules hit the walls more often than slower-moving molecules. The number of collisions each molecule makes with the wall is proportional to the molecule s speed. Second, the force exerted when a molecule strikes the wall depends on the molecule s speed. A fast-moving molecule exerts a larger force than the same molecule moving slower. Force per collision increases with speed, and number of collisions increase with speed, so the total effect of a single molecule on the pressure of a gas is proportional to the square of its speed. 

Pressure is proportional to the square of molecular speed, which in turn is proportional to temperature. For an ideal gas, then, the pressure is directly proportional to temperature, and a plot of P vs. T yields a straight line. Again, this agrees with the ideal gas equation. 

Rates of molecular motion are directly proportional to molecular speeds, so Equation predicts that for any gas, rates of effusion and diffusion increase with the square root of the temperature in kelvins. Also, at any particular temperature, effusion and diffusion are faster for molecules with small molar masses. 

C05-0115. Consider two gas bulbs of equal volume, one filled with H2 gas at 0 °C and 2 atm, the other containing O2 gas at 25 °C and 1 atm. Which bulb has (a) more molecules (b) more mass (c) higher average kinetic energy of molecules and (d) higher average molecular speed ... 

The distribution function (24) for an ideal gas, shown in figure 6 is known as the Maxwell-Boltzmann distribution and is specified more commonly [118] in terms of molecular speed, as... 

D) Whether you can answer this question depends on whether you are acquainted with what is known as the Maxwell-Boltzmann distribution. This distribution describes the way that molecular speeds or energies are shared among the molecules of a gas. If you missed this question, examine the following figure and refer to your textbook for a complete description of the Maxwell-Boltzmann distribution. 

In Eq. (PP), N is the gas concentration (molecules cm 3), um is the average molecular speed in the gas phase, R is the gas constant (J K 1 mol ), T the temperature (K), and M is the molecular weight (kg) of the gas. The normalized rates, i.e., divided by the rate of gas-surface collisions in Eq. (PP), will be referred to as conductances, T, for reasons that will become apparent shortly. However, the reader should keep in mind that these conductances just reflect the speeds of the individual processes. 

From basic statistical-thermodynamics arguments [60] the mean molecular speed in a gas can be determined approximately from the relationship between pressure and mass density as... 

I hope you all understand the mistake Jane made. She trusted John. But if she had it all to do over again, what could Jane have done differently She has to drive the compressor by a fixed-speed motor. The gas molecular weight is going to be unpredictable. The pressure in the wet-gas drum has to be kept constant. 

The average kinetic energy per gas molecule, ( mu2)avg, is independent of the nature of the gas and is directly proportional to the temperature. In this case, the kinetic energy is defined by the standard physical formula in terms of molecule mass, m, and the molecular speed, u. This statement may be taken as a more exact definition of temperature than the qualitative one given in Chapter 1. A list of some common energy units is given in Table 6-1. 

Another quantity which is closely related to the average molecular speed is the speed of sound, which we will write as 5SOund- As noted in Chapter 3, sound waves are actually waves of gas pressure (Figure 3.6)—the density of gas molecules is alternately slightly higher or lower than the equilibrium value. This disturbance travels at a characteristic speed which is clearly not very different from the average molecular speed, but getting the precise numerical value requires a fairly sophisticated treatment. The answer turns out to be... 

Intermolecular collisions do not cause large deviations from the ideal gas law at STP for molecules such as N2 or He, which are well above their boiling points, but they do dramatically decrease the average distance molecules travel to a number which is far less than would be predicted from the average molecular speed. Collisions randomize the velocity vector many times in the nominal round trip time, leading to diffusional effects as discussed in Chapter 4. If all of the molecules start at time t = 0 at the position x = 0, the concentration distribution C(x,t) at later times is a Gaussian ... 

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