For a gas at 300 K, if the RMS speed is 500 m/s, what will be the RMS speed at 6

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Question: For a gas at 300 K, if the RMS speed is 500 m/s, what will be the RMS speed at 600 K?

Options:

Correct Answer: 707 m/s

Solution:

RMS speed is proportional to the square root of temperature, so v_rms at 600 K = 500 * sqrt(600/300) = 707 m/s.

For a gas at 300 K, if the RMS speed is 500 m/s, what will be the RMS speed at 600 K?

For a gas at 300 K, if the RMS speed is 500 m/s, what will be the RMS speed at 600 K?

Step 1: Understand that RMS speed (v_rms) is related to temperature (T) by the formula v_rms ∝ √T.
Step 2: Identify the initial temperature (T1) which is 300 K and the initial RMS speed (v_rms1) which is 500 m/s.
Step 3: Identify the new temperature (T2) which is 600 K.
Step 4: Use the proportionality to find the new RMS speed (v_rms2) using the formula: v_rms2 = v_rms1 * √(T2/T1).
Step 5: Substitute the values into the formula: v_rms2 = 500 * √(600/300).
Step 6: Simplify the fraction inside the square root: 600/300 = 2.
Step 7: Calculate the square root: √2 ≈ 1.414.
Step 8: Multiply 500 by 1.414 to find v_rms2: v_rms2 ≈ 707 m/s.

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, which is a key concept in kinetic theory.