If the RMS speed of a gas is 300 m/s at 300 K, what will be its RMS speed at 600

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Question: If the RMS speed of a gas is 300 m/s at 300 K, what will be its RMS speed at 600 K?

Options:

Correct Answer: 300√2 m/s

Solution:

The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 300 * sqrt(2) m/s.

If the RMS speed of a gas is 300 m/s at 300 K, what will be its RMS speed at 600 K?

If the RMS speed of a gas is 300 m/s at 300 K, what will be its RMS speed at 600 K?

Step 1: Understand that RMS speed (Root Mean Square speed) is related to temperature in gases.
Step 2: Know that the RMS speed is proportional to the square root of the temperature. This means if you double the temperature, the RMS speed increases by the square root of 2.
Step 3: Identify the initial temperature (300 K) and the new temperature (600 K).
Step 4: Calculate the ratio of the new temperature to the old temperature: 600 K / 300 K = 2.
Step 5: Find the square root of this ratio: sqrt(2).
Step 6: Multiply the original RMS speed (300 m/s) by sqrt(2) to find the new RMS speed: 300 m/s * sqrt(2).
Step 7: Conclude that the new RMS speed at 600 K is 300 * sqrt(2) 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, as described by the equation v_rms = sqrt(3kT/m) where k is the Boltzmann constant, T is the temperature, and m is the molar mass.