What is the relationship between the root mean square speed of gas molecules and

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Question: What is the relationship between the root mean square speed of gas molecules and the temperature of the gas?

Options:

Correct Answer: It is directly proportional to the square root of temperature.

Solution:

The root mean square speed of gas molecules is directly proportional to the square root of the absolute temperature of the gas.

What is the relationship between the root mean square speed of gas molecules and the temperature of the gas?

What is the relationship between the root mean square speed of gas molecules and the temperature of the gas?

Step 1: Understand that gas molecules are always moving and their speed can be measured.
Step 2: Learn about temperature, which is a measure of how hot or cold something is.
Step 3: Know that absolute temperature is measured in Kelvin, which starts at absolute zero.
Step 4: The root mean square speed is a way to calculate the average speed of gas molecules.
Step 5: The formula for root mean square speed (v_rms) is v_rms = sqrt(3kT/m), where k is a constant, T is the absolute temperature, and m is the mass of the gas molecules.
Step 6: Notice that the formula shows that as temperature (T) increases, the root mean square speed (v_rms) also increases.
Step 7: Conclude that the root mean square speed of gas molecules is directly related to the square root of the absolute temperature.

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