A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?
Practice Questions
1 question
Q1
A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?
400 m/s
400 sqrt(2) m/s
800 m/s
200 m/s
The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(600/300) = 400 * sqrt(2) m/s.
Questions & Step-by-step Solutions
1 item
Q
Q: A gas at 300 K has an RMS speed of 400 m/s. What will be its RMS speed at 600 K?
Solution: The RMS speed is proportional to the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(600/300) = 400 * sqrt(2) m/s.
Steps: 7
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).
