Thermodynamics, Statistical Thermodynamics, & Kinetics
Thermodynamics, Statistical Thermodynamics, & Kinetics
3rd Edition
ISBN: 9780321766182
Author: Thomas Engel, Philip Reid
Publisher: Prentice Hall
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Chapter 3, Problem 3.21NP
Interpretation Introduction

Interpretation:The expression for the total differential dP in terms of dV and dT needs to be determined for the van der Waals equation of state. This needs to be determined whether dP is an exact differential or not.

Concept Introduction: Thermodynamics is the branch of chemistry that deals with heat exchange between system and surroundings. The thermodynamic process can be classified in two types: isothermal and adiabatic process.

Different thermodynamic properties like enthalpy, entropy, free energy etc. are used to define different properties like volume, pressure and heat capacity.

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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.
(a) Write expressions for dV and dp given that V is a function of p and T and p is a function of V and T. (b) Deduce expressions for d ln V and d ln p in terms of the expansion coefficient and the isothermal compressibility.
The maximum in the Maxwell–Boltzmann distribution occurs when df(v)/dv = 0. Find, by differentiation, an expression for the most probable speed of molecules of molar mass M at a temperature T.

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Thermodynamics, Statistical Thermodynamics, & Kinetics

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