Lecture 2 Summary

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Lecture 2 Summary
Summary 1) The Zeroth Law Systems that have no
tendency to transfer heat are at the
same temperature. 2) Work A process which
transfers energy to or from a system by applying
a force to cause a displacement. 3) Heat A
process which transfers energy between two
systems at different temperatures. 4) The First
Law Energy is conserved for all processes. 5)
The Second Law The entropy of the universe
increases for all processes except
reversible ones, for which there is no change in
Suniv. 6) The absolute temperature scale relates
two temperatures by the heat flow of a Carnot
cycle at those temperatures. 7) The Third Law
There exists a zero of temperature which is
unobtainable and at which the change in entropy
for any process becomes zero.
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Lecture 3 Equilibrium
Main Points 1) Definitions (system, phase,
component) 2) Reversible processes produce no
entropy 3) Infinitesimal processes about
equilibrium points are reversible 4) Energy
functions 5) Criteria for reversibility in
different systems
The concept of equilibrium plays an important
role in thermodynamics. Here we explore the
meaning of equilibrium and the related concept of
reversibility afterdefining some important
terms.
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Additional Definitions
Definitions A chemical system is any system
made up of one or more elements. We generally
restrict ourselves to interest in the bulk
physical and chemical properties for simplicity,
although we could extend our treatment to other
properties, including stress, surface
properties, etc. A phase is any distinguishable
region of a chemical system which is in a
well-defined state of internal equilibrium.
Phases can be open or closed depending on whether
they change or do not change the amount of
material in the phase, respectively. A component
is any independently variable chemical species of
the system For example, P in Si, Ga and As,
(C2H5)OH in H2O.
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Criteria for Equilibrium
Remember, that disorder can never be destroyed
once created and thus for a processto be
reversible it must create no entropy.
Result
Process
Irreversible processes are also called
spontaneous or natural
For irreversible processes For reversible
processes Never
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The Equilibrium Postulate
In a system that is in internal equilibrium, any
infinitesimal process about a point of
equilibrium is reversible.
T1
T2
An infinitesimal change in a system introduces no
finite driving forces and thus no dissipative
processes if the systemis in equilibrium.
T3
Examples of reversible and irreversible
processes? Striking a match Expansion of a gas
into a vacuum Slow expansion of a gas in a
cylinder with a piston Slow stretch of a rubber
band Drop of dye in a swimming pool
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The Equilibrium Postulate
For an infinitesimal process performed on a
single-phase closed chemical system
If the process is reversible we can substitute
From our definition of entropy
In a simple chemical system only mechanical
work is done.
If the process is reversible then T is well
defined for the process and wecan relate the
heat flow to the temperature and change in
entropy.
If the process is reversible then P is well
defined for the process and wecan relate the
mechanical work done on the system to the volume
and pressure.
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The Equilibrium Postulate
So for a closed simple system in internal
equilibrium a reversible infinitesimal process
changes the internal energy by an amount
To generalize this to an open system we need to
take into account the amount the internal energy
changes as the amount of matter in the system
changes. We do this generally by adding the term
If the system is open, then removing a small
amount of material removes the internalenergy
of that part of the material (U is extensive).
n
dn
Where we define the derivative of U with respect
to the amount of component i at constant S, V
and the amount of other components as the
chemical potential
Then
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Energy Functions
Internal Energy
We can define three additional energy functions
using Legendre transformations on our expression
for the change in internal energy
Enthalpy Helmholtz Free Energy Gibbs Free Energy
dP0? dT0?
Substituting in dU
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Criteria for Reversibility
The mathematical form of the Second Law states
that
And for an infinitesimal,reversible process
M
Work W
If the process involves a reversible transfer
of an infinitesimal amount of heat then
Heat Q
Gas
On substitution
And for a chemical system we can substitute in
Criteria for Reversibility
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Isolated System
If a system is isolated, it cannot interact with
the surroundings. The system cannot do work, or
have work done on it nor can it change its
internal energy (the First Law).
General criteria for reversibility
Energy can only be transferred. It cannot be
created or destroyed. Thus, for an isolated
system the internal energy is a constant.
The volume of an isolated system cannot change
Equilibrium is reached in an isolated system
when it maximizes its entropy.
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Closed Isometric and Isothermal System
For a closed, isometric and isothermal system
heat can flow in or out, although the
temperature, volume and amount of material are
constant dV0, dT0 and dni0
Inserting the constant volume expression into the
criteria for equilibrium
Since dT 0
Then on substitution
And from our expression for the Helmholtz Free
energy
Equilibrium is reached in a closed isometric and
isothermal system when it minimizes F.
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Closed Isobaric and Isothermal System
For a closed isobaric and isothermal system, heat
can flow into or out of the system, but the
pressure, temperature, and amount of material are
constant dP0, dT0 and dni0
Then
Substituting the following into our expression
for the equilibrium
From our expression for the Gibbs Free energy
We see that
Equilibrium is reached in a closed isothermal,
isobaric system when it minimizes G.
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Lecture 3 Equilibrium
Main Points 1) Definitions (chemical system,
phase, component) 2) Reversible processes produce
no entropy 3) Infinitesimal processes about
equilibrium points are reversible 4) Energy
functions U, H, F, and G 5) Criteria for
reversibility in different systems
The concept of equilibrium plays an important
role in thermodynamics. We havederived criteria
that must be satisfied for systems under various
conditions for them to be in equilibrium.