What is the relationship between RMS speed and kinetic energy of gas molecules?

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Question: What is the relationship between RMS speed and kinetic energy of gas molecules?

Options:

Correct Answer: Directly proportional

Solution:

The kinetic energy of gas molecules is directly proportional to the square of the RMS speed, as KE = (1/2)mv_rms^2.

What is the relationship between RMS speed and kinetic energy of gas molecules?

What is the relationship between RMS speed and kinetic energy of gas molecules?

Step 1: Understand that gas molecules are always moving and have kinetic energy due to their motion.
Step 2: Learn that RMS speed (Root Mean Square speed) is a way to measure the average speed of gas molecules.
Step 3: Know the formula for kinetic energy (KE) of an object, which is KE = (1/2)mv^2, where m is mass and v is speed.
Step 4: Replace v in the kinetic energy formula with v_rms (the RMS speed) to get KE = (1/2)m(v_rms)^2.
Step 5: Notice that the kinetic energy depends on the square of the RMS speed, meaning if the RMS speed increases, the kinetic energy increases even more.

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