![which of the following provides a measure of the average speed of air molecules? which of the following provides a measure of the average speed of air molecules?](https://acp.copernicus.org/articles/20/4809/2020/acp-20-4809-2020-avatar-web.png)
Since there are many molecules and since there is no preferred direction, the average square of the velocities in the x, y and z-direction are equal For every molecule the total velocity can be calculated easily Where M is the molecular weight of the gas. The term in parenthesis can be rewritten in terms of the average square velocity: The pressure exerted by the gas is equal to the force per unit area, and therefore The force exerted on the wall by this molecule can be calculated easilyįor n moles of gas, the corresponding force is equal to The time required to complete this path is given byĮach time the molecule collides with the right wall, it will change the momentum of the wall by ∆p. The change in the momentum of the particle is thereforeĪfter the molecule is scattered of the right wall, it will collide with the left wall, and finally return to the right wall. The y and z components of the momentum of the molecule are left unchanged.
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The result of the collision is a reversal of the direction of the x-component of the momentum of the molecule: The molecule will collide with the right wall. Figure 18.1 shows a molecule moving in the box. The molecules in the box move in all directions with varying speeds, colliding with each other and with the walls of the box. Let n moles of an ideal gas be confined to a cubical box of volume V. Pressure and Temperature: A Molecular View since only their ratio enter the equation. The units for the volume and pressure can be left in l and atm. The temperature T in this formula must be expressed in Kelvin: The initial state of the gas is specified by V i, p i and T i the final state of the gas is specified by V f, p f and T f. The temperature is raised to 35 ° C, and the volume is reduced to 8.5 l. Since T is kept constant, the work done can be calculated easilyĪ cylinder contains oxygen at 20 ° C and a pressure of 15 atm. The ideal gas law provides us with a relation between the pressure and the volume The work done by the expanding gas is given by During the expansion the temperature T of the gas is kept constant (this process is called isothermal expansion ). Suppose a sample of n moles of an ideal gas is confined in an initial volume V i. Using the ideal gas law we can calculate the work done by an ideal gas. The temperature of the gas must always be expressed in absolute units (Kelvin). Where n is the number of moles of gas, and R is the gas constant. Experiments showed that the gases obey the following relation (the ideal gas law ): Reversely, if we take 1 mole samples of various gases, confine them in boxes of identical volume and hold them at the same temperature, we find that their measured pressures are nearly identical. The number of moles in a sample, n, can be determined easily:Īvogadro made the suggestion that all gases - under the same conditions of temperature and pressure - contain the same number of molecules. This number is called the Avogadro constant, N A. Laboratory experiments show that the number of atoms in a 12-g sample of 12 C is equal to 6.02 x 10 23 mol -1. " the amount of any substance that contains as many atoms/molecules as there are atoms in
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The mole is a measure of the number of molecules in a sample, and it is defined as In relating the effects of the motion of atoms and molecules to macroscopic observables like pressure and temperature, we have to determine the number of molecules in the gas. It is however clear that the pressure exerted by a gas is related to the linear momentum of the atoms and molecules, and that the temperature of the gas is related to the kinetic energy of the atoms and molecules. The laws of classical thermodynamics do not show the direct dependence of the observed macroscopic variables on microscopic aspects of the motion of atoms and molecules.