a) Briefly explain the physical processes that lead to an equilibrium value for the volume V of a solid. b) Potassium chloride is an ionic salt, whose internal energy per mole is well-modelled by the function aN₁Q+Q™ Απερ +6Be-r/ro, where a is the Madelung constant for this material, Q are the electric charges of the potassium (K+) and chloride (Cl-) ions, N₁ is Avogrado's number, r the closest distance between oppositely charged ions, and to the permittivity of free space. We have introduced the constants B and ro. €0 U(r) = Explain the physical origin of the two terms in this equation.

a) Briefly explain the physical processes that lead to an equilibrium value for the volume V of a solid. b) Potassium chloride is an ionic salt, whose internal energy per mole is well-modelled by the function aN₁Q+Q™ Απερ +6Be-r/ro, where a is the Madelung constant for this material, Q are the electric charges of the potassium (K+) and chloride (Cl-) ions, N₁ is Avogrado's number, r the closest distance between oppositely charged ions, and to the permittivity of free space. We have introduced the constants B and ro. €0 U(r) = Explain the physical origin of the two terms in this equation.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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Concept explainers

Chemical and Phase Equilibrium

Phase diagrams or equilibrium phase diagrams are the graphical representations that show the phase transformations of the constituting elements with respect to the pressure, temperature, and compositions. The diagrams show the conditions that limit the different phases, namely solid, liquid, and gas. The diagram can also be utilized to verify the relations between the state variables. Most of the phase diagrams are temperature-pressure phase diagrams, with the variable parameter as the composition. Usually other variables such as solubility and pressure parameters are not indicated in the phase diagram. For a one-component system (unary phase diagram), the phase diagram is generally a function of temperature and pressure as the state variables, or temperature and volume. However, for a binary system (two-phase) having two components, the phase diagram is a function of temperature and composition as the state variables only. Coexisting of the different phases of the constituting elements is indicated in the phase diagram. A ternary phase diagram can be characterized by consisting of three phases in equilibrium.

Question

a) Briefly explain the physical processes that lead to an equilibrium value for the volume V of
a solid.
b)
Potassium chloride is an ionic salt, whose internal energy per mole is well-modelled by the
function
aN₁Q+Q™
4π€0 r
+6Be-r/ro
where a is the Madelung constant for this material, Q are the electric charges of the
potassium (K+) and chloride (Cl-) ions, N₁ is Avogrado's number, r the closest distance
between oppositely charged ions, and the permittivity of free space. We have introduced
the constants B and ro.
U(r)
=
Explain the physical origin of the two terms in this equation.
U = -
c) By assuming that potassium chloride has the same structure as sodium chloride, explain
why the internal energy per mole may be written in terms of the volume V as
-1/3
aNte² (2NA)
(2N₁)
4π€0
+6B exp
1
[]
To 2NA

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