The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ 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 −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.

The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ 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 −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter2: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 2.92E

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