A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?

A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?

Correct Answer: 565.69 m/s

Step 1: Understand that RMS speed (Root Mean Square speed) is related to temperature.
Step 2: Know that the RMS speed is proportional to the square root of the temperature.
Step 3: Identify the initial temperature (T1) which is 300 K and the final temperature (T2) which is 600 K.
Step 4: Calculate the ratio of the final temperature to the initial temperature: T2/T1 = 600 K / 300 K = 2.
Step 5: Take the square root of the ratio: sqrt(2).
Step 6: Multiply the initial RMS speed by the square root of the temperature ratio: 400 m/s * sqrt(2).
Step 7: This gives the new RMS speed at 600 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, as described by the equation v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas particles.