For an ideal gas, if the temperature is increased, what happens to the RMS speed

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Question: For an ideal gas, if the temperature is increased, what happens to the RMS speed?

Options:

Correct Answer: Increases

Solution:

The RMS speed increases with temperature as v_rms = sqrt(3RT/M) shows that it is directly proportional to the square root of temperature T.

For an ideal gas, if the temperature is increased, what happens to the RMS speed?

For an ideal gas, if the temperature is increased, what happens to the RMS speed?

Step 1: Understand what RMS speed is. RMS speed is a measure of the average speed of gas particles in an ideal gas.
Step 2: Know the formula for RMS speed: v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature, and M is the molar mass of the gas.
Step 3: Identify the relationship between temperature (T) and RMS speed (v_rms) in the formula. The formula shows that v_rms is proportional to the square root of T.
Step 4: Realize that if the temperature (T) increases, the square root of T also increases.
Step 5: Conclude that since v_rms is directly proportional to the square root of T, an increase in temperature will lead to an increase in RMS speed.

Ideal Gas Law – Understanding the relationship between temperature, pressure, volume, and the behavior of ideal gases.
RMS Speed – The root mean square speed of gas molecules, which is influenced by temperature.
Direct Proportionality – Recognizing that RMS speed is directly proportional to the square root of temperature.