Question

What does the Maxwell speed distribution curve tell us? Does Maxwell's theory work for a sample of 200 molecules? Explain.

Short answer

The Maxwell speed distribution curve reveals that at any given temperature, gas molecules possess a wide range of speeds, with a particular speed at which the maximum number of molecules move. While Maxwell's theory gives accurate predictions for large numbers of molecules, it may not perfectly apply to a small sample due to statistical fluctuations.

Step-by-step solution

Understanding the Maxwell speed distribution curve

In Kinetic Theory, the Maxwell speed distribution curve is a statistical means of representing the speeds of gas molecules in a given sample at a specific temperature. The speed distribution is presented in a graph where the x-axis signifies the speed (or velocity) and the y-axis represents the number of molecules. The curve tells us that at any given temperature, gas molecules have a wide range of speeds, from quite slow to extremely fast. It also indicates that there's a particular speed (most probable speed) at which the maximum number of molecules moves.

Application of Maxwell's theory to a small sample

Maxwell's theory is a statistical theory which means it applies to larger samples of molecules. The statistical approach considers the average behavior of a large number of particles. Thus, for a sample of only 200 molecules, the distribution may not be perfect and the most probable speed that Maxwell's theory predicts might not be the most common speed in such a small sample. This is due to statistical fluctuations, where the smaller the sample, the larger the relative fluctuations. In statistical mechanics, it is assumed that a macroscopic system consists of a very large number of particles. That is not the case for a sample of 200 molecules.