Let ¯¯¯v,vrms and vp, respectively, denote the mean speed, root mean square speed and most probable speed of the molecules in an ideal monatiomc gas at absolute temperature T. The mass of a molecules is m. Then
No molecule can have speed less than vp/√2
No molecule can have a speed greater than √2vrms
vp<¯¯¯v<vrms
The average kinetic energy of a molecule is 34mv2P
A
vp<¯¯¯v<vrms
B
No molecule can have a speed greater than √2vrms
C
No molecule can have speed less than vp/√2
D
The average kinetic energy of a molecule is 34mv2P
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Solution
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vrms=√3RTM,¯¯¯v=√8π⋅RTM≈√2.5RTM and vp=√2RTM From these expressions we can see that vp<¯¯¯v<vrms Second, vrms=√32vp and average kinetic energy of a gas molecule =12mv2rms =12m(√32vp)2=34mv2p.
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