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If the temperature of a gas is increased from 300 K to 600 K, how does the RMS s
If the temperature of a gas is increased from 300 K to 600 K, how does the RMS speed change?
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Practice Questions
1 question
Q1
If the temperature of a gas is increased from 300 K to 600 K, how does the RMS speed change?
It doubles
It increases by sqrt(2)
It increases by sqrt(3)
It remains the same
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RMS speed is proportional to the square root of temperature. Increasing from 300 K to 600 K increases the speed by sqrt(2).
Questions & Step-by-step Solutions
1 item
Q
Q: If the temperature of a gas is increased from 300 K to 600 K, how does the RMS speed change?
Solution:
RMS speed is proportional to the square root of temperature. Increasing from 300 K to 600 K increases the speed by sqrt(2).
Steps: 6
Show Steps
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.
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