Ch.10 - Gases

Problem 9c

Chapter 10, Problem 9c

Consider the following graph. (c) For each curve, which speed is highest: the most probable speed, the root-mean-square speed, or the average speed?

Verified step by step guidance

insert step 1: Understand the three types of molecular speeds in a gas: the most probable speed (v_p), the average speed (v_avg), and the root-mean-square speed (v_rms).

insert step 2: Recall the relationships between these speeds: v_p < v_avg < v_rms for a given temperature.

insert step 3: Analyze the graph to identify the curves representing each of these speeds.

insert step 4: Compare the positions of the peaks and the spread of the curves to determine which speed is highest for each curve.

insert step 5: Conclude that the root-mean-square speed is typically the highest among the three speeds for each curve.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Most Probable Speed

The most probable speed is the speed at which the maximum number of particles in a gas sample are moving at a given temperature. It is derived from the Maxwell-Boltzmann distribution and represents the peak of the distribution curve, indicating the most common speed among the particles.

Root-Mean-Square Speed

The root-mean-square (RMS) speed is a measure of the average speed of particles in a gas, calculated as the square root of the average of the squares of the speeds. It provides a way to quantify the kinetic energy of the gas particles and is always greater than or equal to the average speed.

Average Speed

The average speed of gas particles is calculated by taking the total distance traveled by all particles divided by the total time taken. It is a straightforward arithmetic mean and typically falls between the most probable speed and the root-mean-square speed, reflecting the overall motion of the gas.

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