If the temperature of a gas is doubled, what happens to its RMS speed?
Practice Questions
1 question
Q1
If the temperature of a gas is doubled, what happens to its RMS speed?
Increases by a factor of sqrt(2)
Increases by a factor of 2
Increases by a factor of sqrt(3)
Remains the same
The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).
Questions & Step-by-step Solutions
1 item
Q
Q: If the temperature of a gas is doubled, what happens to its RMS speed?
Solution: The RMS speed is proportional to the square root of the temperature. If the temperature is doubled, the RMS speed increases by a factor of sqrt(2).
Steps: 6
Step 1: Understand that RMS speed stands for Root Mean Square speed, which is a measure of the average speed of gas particles.
Step 2: Know that the RMS speed of a gas is related to its temperature. Specifically, it is proportional to the square root of the temperature.
Step 3: If the temperature of the gas is doubled, we can express this mathematically as T' = 2T, where T is the original temperature and T' is the new temperature.
Step 4: Since RMS speed (v_rms) is proportional to the square root of the temperature, we can write v_rms ∝ √T.
Step 5: When the temperature is doubled, the new RMS speed becomes v_rms' ∝ √(2T) = √2 * √T.
Step 6: This means that the new RMS speed is √2 times the original RMS speed, indicating that the RMS speed increases by a factor of √2.
