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Question

# Graph shows a hypothetical speed distribution for a sample of N gas particle (for V>V0;dNdV=0,dNdV is a rate of change of number of particles with change velocity).

A
The value of aV0 is 2N
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B
The ratio Vavg/V0 is equal to 2/3
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C
The ratio Vrms/V0 is equal to 1/2
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D
Three fourth of the total particle has a speed between 0.5 V0 and V0
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Solution

## The correct option is A The value of aV0 is 2NThe graph dNdV vs V is lincar, whose slope is given by :m=av0 [From graph]So, equation of the graph can be through as :y=mx+c (Equation of straight line)As graph passes through origin, c - 0 (y - intercept)]So we have y=dNdV and x=V in this graph.⇒dNdV=aV0v⇒dV=aV0vdvIntegrating both sides in limit 0→N as V:0→v0⇒∫N0dN=∫v00aV0vdv⇒[N]N0=aV0[v22]v00⇒N=aV0.V022That gives,⇒aV0=2N

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