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Question

The graph shows hypothetical speed distribution for a sample of 𝑁 gas particles (for V0, dNdV=0)


A
The value of aV0 is 2N
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B
The ratio VavgV0 is equal to 23
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C
The ratio VrmsV0 is equal to 12
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D
Three-fourths of the total particles have a speed between 0.5V0 and V0
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Solution

The correct options are
A The value of aV0 is 2N
B The ratio VavgV0 is equal to 23
C The ratio VrmsV0 is equal to 12
D Three-fourths of the total particles have a speed between 0.5V0 and V0

a)

dNdVvdNdv=av0v

av0=2 (Area under the curve)

Area= ydx=dNdv.dv=dN=N

b)

dNdv=avv0

dNavv0dv

vavg=dNvdN

vavg=v00avv0dvvv0avv0dv

vavg=av0v00v2dvav0vv00vdv=2V03

c)

vrms=mean sq

mean sq=dNv2dN

mean sq=V00avv0dvv2V00avv0dv

V00v3dvV00vdv=v404V204=0.5V20

vrms=12v20Vrms=v02Vrmsv0=12


v02+v034Number of molequles.


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