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ME 311
THERMODYNAMICS
S. Masutani
FALL 2007
1
CHAPTER 5 (continued)
To be able to apply the 2
nd
Law in analyses of systems we must be able to evaluate entropy as a
function of state.
2 ways:
1.
Determine the probabilities of energy microstates and apply the results of quantum–
statistical mechanics to evaluate S from spectroscopic and other data on the molecules of
the system.
2.
Determine entropy from macroscopic laboratory data (averaged over many molecules and
molecular events over a “long” period of time–relative to the molecular timescales),
utilizing relationships between S and other thermodynamic variables which can be
evaluated directly.
The Statistical Definition of Entropy (modern)
(nonrigorous derivation)
The underlying concept in our pursuit of a formulation for entropy is that the total energy of a
system under study, i.e., a quantity of matter, is the sum of the energy retained by each of the
constituent molecules (or atoms).
In a classical description, each particle is described by
continuous position coordinates and corresponding momenta.
Energy appears as a continuous
function of these variables (position; momenta).
Entropy reflects our uncertainty about the
distribution of the molecules of the system in this position–momentum space.
Quantum mechanics has shown that, at the microscopic level, matter exists only in discreet
quantum states.
Statistical thermodynamics has incorporated this “new” understanding into its
established framework:
the total energy, E, of a system corresponds to some distribution of N
particles among the permissible energy states
ε
1
,
ε
2
, …,
ε
i
,….
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 Fall '07
 Masutani

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