If the temperature of a gas is increased from 200 K to 800 K, how does the RMS s

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Question: If the temperature of a gas is increased from 200 K to 800 K, how does the RMS speed change?

Options:

Correct Answer: Increases by sqrt(4)

Solution:

RMS speed increases by sqrt(4) = 2, since v_rms is proportional to sqrt(T).

If the temperature of a gas is increased from 200 K to 800 K, how does the RMS speed change?

If the temperature of a gas is increased from 200 K to 800 K, how does the RMS speed change?

Step 1: Understand that RMS speed (v_rms) of a gas is related to its temperature (T).
Step 2: Know the formula that relates RMS speed to temperature: v_rms is proportional to the square root of temperature (v_rms ∝ √T).
Step 3: Identify the initial temperature (T1) as 200 K and the final temperature (T2) as 800 K.
Step 4: Calculate the ratio of the final temperature to the initial temperature: T2 / T1 = 800 K / 200 K = 4.
Step 5: Since v_rms is proportional to the square root of temperature, find the square root of the ratio: √(T2 / T1) = √4 = 2.
Step 6: Conclude that the RMS speed increases by a factor of 2 when the temperature increases from 200 K to 800 K.

RMS Speed and Temperature Relationship – The root mean square (RMS) speed of a gas is directly proportional to the square root of its absolute temperature (T), as described by the equation v_rms ∝ √T.