If the temperature of a gas is doubled, how does its RMS speed change?
Practice Questions
1 question
Q1
If the temperature of a gas is doubled, how does its RMS speed change?
Increases by a factor of sqrt(2)
Increases by a factor of 2
Increases by a factor of 4
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, how does its RMS speed change?
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: 7
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. The formula is: RMS speed = sqrt(3 * k * T / m), where T is the temperature.
Step 3: Recognize that if the temperature (T) is doubled, we can express this as T' = 2T.
Step 4: Substitute the new temperature into the RMS speed formula: RMS speed' = sqrt(3 * k * (2T) / m).
Step 5: Simplify the equation: RMS speed' = sqrt(2) * sqrt(3 * k * T / m).
Step 6: Notice that sqrt(3 * k * T / m) is the original RMS speed. Therefore, RMS speed' = sqrt(2) * (original RMS speed).
Step 7: Conclude that when the temperature is doubled, the RMS speed increases by a factor of sqrt(2).
