If the temperature of a gas is halved, what happens to its RMS speed?
Practice Questions
1 question
Q1
If the temperature of a gas is halved, what happens to its RMS speed?
Increases by sqrt(2)
Decreases by sqrt(2)
Remains the same
Decreases by 2
RMS speed is directly proportional to the square root of temperature. Halving the temperature results in a decrease in RMS speed by sqrt(2).
Questions & Step-by-step Solutions
1 item
Q
Q: If the temperature of a gas is halved, what happens to its RMS speed?
Solution: RMS speed is directly proportional to the square root of temperature. Halving the temperature results in a decrease in RMS speed by sqrt(2).
Steps: 8
Step 1: Understand that RMS speed refers to the root mean square speed of gas particles.
Step 2: Know that the RMS speed is directly related to the temperature of the gas.
Step 3: Recall the formula for RMS speed: v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas particles.
Step 4: If the temperature (T) is halved, we can express this as T' = T/2.
Step 5: Substitute T' into the RMS speed formula: v_rms' = sqrt(3k(T/2)/m).
