The cohesive energy density, V, is defined as U/V, where U is the mean potential energy

Chapter 18, Problem 18.15

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The cohesive energy density, V, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that V = 12 N V(R)d, where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form C6 /R6 is equal to (2/3)(NA 2 /d3M2) 2C6, where is the mass density of the solid sample and Mis the molar mass of the molecules.