Category: The Kinetic Theory of Gases

We saw in Section 17-4 that sound waves are propagated through air and other gases as a series of compressions and expansions; these variations in the transmission medium take place so rapidly that there is no time for energy to be transferred from one part of the medium to another as heat. As we saw in Section 17-11,…

We can improve the agreement of kinetic theory with experiment by including the oscillations of the atoms in a gas of diatomic or polyatomic molecules. For example, the two atoms in the O2 molecule of Fig. 19-11b can oscillate towardand away from each other, with the interconnecting bond acting like a spring. However, experiment shows that such oscillations…

As Table 19-2 shows, the prediction that  agrees with experiment for monatomic gases but fails for diatomic and polyatomic gases. Let us try to explain the discrepancy by considering the possibility that molecules with more than one atom can store internal energy in forms other than translational kinetic energy. Figure 19-11 shows common models of helium (a monatomic molecule, containing a…

In this section, we want to derive from molecular considerations an expression for the internal energy Eint of an ideal gas. In other words, we want an expression for the energy associated with the random motions of the atoms or molecules in the gas. We shall then use that expression to derive the molar specific heats of…

The root-mean-square speed vrms gives us a general idea of molecular speeds in a gas at a given temperature. We often want to know more. For example, what fraction of the molecules have speeds greater than the rms value? What fraction have speeds greater than twice the rms value? To answer such questions, we need to know…

We continue to examine the motion of molecules in an ideal gas. Figure 19-4 shows the path of a typical molecule as it moves through the gas, changing both speed and direction abruptly as it collides elastically with other molecules. Between collisions, the molecule moves in a straight line at constant speed. Although the figure shows the…

We again consider a single molecule of an ideal gas as it moves around in the box of Fig. 19-3, but we now assume that its speed changes when it collides with other molecules. Its translational kinetic energy at any instant is mv2. Its average translational kinetic energy over the time that we watch it is in which we…

Here is our first kinetic theory problem. Let n moles of an ideal gas be confined in a cubical box of volume V, as in Fig. 19-3. The walls of the box are held at temperature T. What is the connection between the pressure p exerted by the gas on the walls and the speeds of the molecules? The molecules of gas…

Our goal in this lesson is to explain the macroscopic properties of a gas—such as its pressure and its temperature—in terms of the behavior of the molecules that make it up. However, there is an immediate problem: which gas? Should it be hydrogen, oxygen, or methane, or perhaps uranium hexafluoride? They are all different. Experimenters…

When our thinking is slanted toward atoms and molecules, it makes sense to measure the sizes of our samples in moles. If we do so, we can be certain that we are comparing samples that contain the same number of atoms or molecules. The mole is one of the seven SI base units and is defined as…