If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600 K?
Practice Questions
1 question
Q1
If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600 K?
400 m/s
800 m/s
400√2 m/s
800√2 m/s
The RMS speed increases with the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(2), which is approximately 800 m/s.
Questions & Step-by-step Solutions
1 item
Q
Q: If the RMS speed of a gas is 400 m/s at 300 K, what will be the RMS speed at 600 K?
Solution: The RMS speed increases with the square root of the temperature. Therefore, at 600 K, the RMS speed will be 400 * sqrt(2), which is approximately 800 m/s.
Steps: 8
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 to temperature: RMS speed is proportional to the square root of the temperature.
Step 3: Identify the initial RMS speed, which is 400 m/s at 300 K.
Step 4: Identify the new temperature, which is 600 K.
Step 5: Calculate the ratio of the new temperature to the old temperature: 600 K / 300 K = 2.
Step 6: Take the square root of this ratio: sqrt(2).
Step 7: Multiply the initial RMS speed by the square root of the temperature ratio: 400 m/s * sqrt(2).
Step 8: Calculate the final RMS speed: 400 * sqrt(2) is approximately 800 m/s.
