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Question

For a gas sample with N number of molecules, function N(V) is given by :
N(V)=dNdV=(3NV3)V2   for 0<V<Vand N(V)=0  for V>Vwhere dN is the number of molecules in the speed range V to V+dV. If the rms speed of the molecules is nV0.Then the value of  n is


Solution

V2rms=<V>=V21+V22+V23+......N=V2dNdN and dNdv=N(V)V2rms=1N0N(V)V2dV=1N0(3NV3.V2)V2dV=35V2Vrms=35V
  n = 35
n = 0.6

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