# Root mean square speed

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#1
I don't really understand the value of the root mean square speed in the molecular kinetic theory of gases, and the AQA endorsed textbook barely touches on it.

I get that taking the root mean square of the velocities of gas molecules compensates for the velocity of the molecules being a vector, but it specifically states to square their speeds rather than their velocities
At that point (and either way) what would be the advantage of using vrms over just the mean of the modulus of the molecules' velocities?

The closest answer I could find was that the kinetic energy of molecules with speeds equal to the vrms is the same as the average kinetic energy of all the molecules in the gas, but if "average kinetic energy" is referring to the mean kinetic energy, why wouldn't the mean kinetic energy just correspond to the mean speed rather than the vrms?
Last edited by nzy; 1 year ago
0
1 year ago
#2
(Original post by nzy)
I don't really understand the value of the root mean square speed in the molecular kinetic theory of gases, and the AQA endorsed textbook barely touches on it.

I get that taking the root mean square of the velocities of gas molecules compensates for the velocity of the molecules being a vector, but it specifically states to square their speeds rather than their velocities
At that point (and either way) what would be the advantage of using vrms over just the mean of the modulus of the molecules' velocities?

The closest answer I could find was that the kinetic energy of molecules with speeds equal to the vrms is the same as the average kinetic energy of all the molecules in the gas, but if "average kinetic energy" is referring to the mean kinetic energy, why wouldn't the mean kinetic energy just correspond to the mean speed rather than the vrms?
This is clearly a question from a v good student and i need time to answer fully
0
1 year ago
#3
(Original post by Swinroy2)
This is clearly a question from a v good student and i need time to answer fully
The short answer is that the mean-squared speed is a brilliantly used variable when calculating the Mean Kinetic Energy:
The problem is that the UNITS of this quantity are not he same as speed, and not easily visualised in terms of speed ...so Scientists decided on taking the SQUARE ROOT of this quantity to give it the same units as SPEED so we have The RMS which is the square root of the MEAN SQUARED SPEED
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