If the temperature of a gas is doubled, what happens to its RMS speed?

₹0.0

Question: If the temperature of a gas is doubled, what happens to its RMS speed?

Options:

Correct Answer: Increases by a factor of sqrt(2)

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).

If the temperature of a gas is doubled, what happens to its RMS speed?

If the temperature of a gas is doubled, what happens to its RMS speed?

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.

RMS Speed and Temperature Relationship – The root mean square (RMS) speed of a gas is directly related to the square root of its absolute temperature, as described by the equation v_rms = sqrt(3kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of the gas particles.