how to derive Vrms=sqrt(3RT/M

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According to pressure equation, PV=1/3 M Vrms².

=>nRT=1/3 M Vrms²

=> T directly proportional to M Vrms²

According to mean Kinetic energy,

KE(avg)=1/2 M Vrms²

=> KE(avg) directly proportional to M Vrms²

This means.. M Vrms² directly proportional to KE(avg) T

=> M Vrms² /T = KE(avg) × proportionality constant

So this means the avg Kinetic energy is inversely proportional to Absolute Temperature. But actually KE(avg) is directly proportional to T. Please clear my doubt

Q. Identify the correct labels of A, B and C in the following graph from the options given below:

Root mean square speed (

V_{r} m s)

; most probable speed

(V_{m} p)

; average speed

(V_{a} v)

Q. Suppose a container is evacuated to leave just one molecule of a gas in it. Let

v_{a v}

and

v_{r m s}

represent the average speed and rms speed of the gas.

Q. Suppose a container is evacuated to leave just one molecule of a gas in it. Let

v_{α}

and

v_{r m s}

represent the average speed and the rms speed of the gas.

Q. Identify the correct order as indicated in the given diagram of different kind of speed of molecules of same gas.

v_{m p} \to

Most probable speed

v_{r m s} \to

Root mean square speed

v_{a v} \to

Average speed

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