What is the relationship between the average speed and RMS speed of a gas?

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Question: What is the relationship between the average speed and RMS speed of a gas?

Options:

Correct Answer: RMS speed is always greater than average speed

Solution:

For an ideal gas, the RMS speed is always greater than the average speed due to the squaring of velocities in the RMS calculation.

What is the relationship between the average speed and RMS speed of a gas?

What is the relationship between the average speed and RMS speed of a gas?

Step 1: Understand what average speed means. It is the total distance traveled by gas particles divided by the number of particles.
Step 2: Understand what RMS speed means. RMS stands for Root Mean Square, which is a way to calculate the average speed that gives more weight to higher speeds.
Step 3: Realize that in the RMS calculation, each speed is squared before averaging. This means that faster particles contribute more to the RMS speed.
Step 4: Compare the two speeds. Since the RMS speed takes into account the squared values, it will always be greater than the average speed for an ideal gas.
Step 5: Conclude that the relationship is that RMS speed is always greater than average speed for an ideal gas.

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