If the temperature of a gas is increased from 300 K to 600 K, how does the RMS s

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Question: If the temperature of a gas is increased from 300 K to 600 K, how does the RMS speed change?

Options:

Correct Answer: It increases by sqrt(2)

Solution:

RMS speed is proportional to the square root of temperature. Increasing from 300 K to 600 K increases the speed by sqrt(2).

If the temperature of a gas is increased from 300 K to 600 K, how does the RMS speed change?

If the temperature of a gas is increased from 300 K to 600 K, how does the RMS speed change?

Step 1: Understand that RMS speed (Root Mean Square speed) of a gas is related to its temperature.
Step 2: Know the formula that relates RMS speed (v_rms) to temperature (T): v_rms is proportional to the square root of T.
Step 3: Identify the initial temperature (T1) as 300 K and the final temperature (T2) as 600 K.
Step 4: Calculate the ratio of the final temperature to the initial temperature: T2 / T1 = 600 K / 300 K = 2.
Step 5: Find the square root of this ratio: sqrt(2).
Step 6: Conclude that the RMS speed increases by a factor of sqrt(2) when the temperature increases from 300 K to 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.