A gas at 300 K has an RMS speed of 500 m/s. What will be its RMS speed at 600 K?

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Question: A gas at 300 K has an RMS speed of 500 m/s. What will be its RMS speed at 600 K?

Options:

Correct Answer: 707 m/s

Solution:

The RMS speed is proportional to the square root of the temperature. Therefore, v_rms at 600 K = 500 * sqrt(600/300) = 500 * sqrt(2) ≈ 707 m/s.

A gas at 300 K has an RMS speed of 500 m/s. What will be its RMS speed at 600 K?

A gas at 300 K has an RMS speed of 500 m/s. What will be its 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 final temperature (T2) which is 600 K.
Step 3: Calculate the ratio of the temperatures: T2/T1 = 600 K / 300 K = 2.
Step 4: Take the square root of the ratio: √(T2/T1) = √2.
Step 5: Multiply the initial RMS speed (500 m/s) by the square root of the temperature ratio: v_rms at 600 K = 500 m/s * √2.
Step 6: Calculate the final RMS speed: v_rms at 600 K ≈ 500 m/s * 1.414 ≈ 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.