Let’s begin by looking at a gas. Do all the molecules in the gas move with the same speed? Or is there a range of speeds? This important question can be answered experimentally.

FIGURE 20.1 shows an experiment to measure the speeds of molecules in a gas. The two rotating disks form a velocity selector. Once every revolution, the slot in the first disk allows a small pulse of molecules to pass through. By the time these molecules reach the second disk, the slots have rotated. The molecules can pass through the second slot and be detected only if they have exactly the right speed $v=L\text{/}\text{Δ}t$ to travel between the two disks during time interval $\text{Δ}t$ it takes the axle to complete one revolution. Molecules having any other speed are blocked by the second disk. By changing the rotation speed of the axle, this apparatus can measure how many molecules have each of many possible speeds.

FIGURE 20.1 An experiment to measure the speeds of molecules in a gas.

FIGURE 20.2 shows the results for nitrogen gas $(\text{N}{}_2)$ at $T=20\text{°}\text{C}$. The data are presented in the form of a histogram, a bar chart in which the height of each bar tells how many (or, in this case, what percentage) of the molecules have a speed in the range of speeds shown below the bar. For example, 16% of the molecules have speeds in the range from $600\text{m}\text{/}\text{s}$ to $700\text{m/s}$. All the bars sum to 100%, showing that this histogram describes all of the molecules leaving the source.

FIGURE 20.2 The distribution of molecular speeds in a sample of nitrogen gas.

It turns out that the molecules have what is called a distribution of speeds, ranging from as low as $\approx 100\text{m}\text{/}\text{s}$ to as high as $\approx 1200\text{m/s}$. But not all speeds are equally likely; there is a most likely speed of $\approx 550\text{m/s}$. This is really fast, $\approx 1200\text{mph}!$ Changing the temperature or changing to a different gas changes the most likely speed, as we’ll learn later in the chapter, but it does not change the shape of the distribution.

If you were to repeat the experiment, you would again find the most likely speed to be $\approx 550\text{m}\text{/}\text{s}$ and that 16% of the molecules have speeds between $600\text{m}\text{/}\text{s}$ and $700\text{m}\text{/}\text{s}$. This is an important lesson. Although a gas consists of a vast number of molecules, each moving randomly, averages, such as the average number of molecules in the speed range 600 to $700\text{m}\text{/}\text{s}$, have precise, predictable values. The micro/macro connection is built on the idea that the macroscopic properties of a system, such as temperature or pressure, are related to the average behavior of the atoms and molecules.