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Ch 21b - A Thermodynamics Primer/Review

23Feb2007

Weve spent most of Ch21b learning about the microscopic world, one thatis defined by quantum mechanics. Such understanding has emerged only

relatively recently within the history of chemistry, much of what we know

about the transformation of chemical systems was gleaned from studies of

macroscopic samples before the advent of the Schrdinger equation.

Chief among these advancements was thermodynamics. The power of this

discipline lies in its generality. The field developed from observations of

the natural world, it stands on its own. No molecular details of the system

under study enter into classical thermodynamic analyses. The desire to bridge

the macroscopic and microscopic worlds lies at the heart ofstatistical

thermodynamics, a subject we will consider for the remainder of the quarter.

Here well briefly review the fundamental laws of thermodynamics, in orderto provide the necessary backdrop for the molecular/statistical analysis that

is based on the collective behavior of extremely large numbers of microscopic

quantum mechanical systems.

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Ch 21b - The Zeroth Law of Thermodynamics

23Feb2007

The quantitative concepts of temperature, work, internal energy, and heat playan important role in the understanding of chemical phenomena. The need to

define an absolute temperature scale was not recognized until after the first

and second laws of thermodynamics were established. Briefly, it states:

For three systems A, B, and C, if A is in thermal equilibrium with C and B is

also in thermal equilibrium with C; then A and B are in thermal equilibrium

with each other.

A C B

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Ch 21b - Thermodynamic State Variables/Functions

23Feb2007

When a system is at equilibrium under a given set of conditions, it is said tobe in a definite state. State variables include things like pressure, volume

and temperature (P, V, T). Those variables that depend on the size of the

system are referred to as extensive (such as V, energy); those that do not

are referred to as intensive (P, T, for example). Extensive variables can beconverted into intensive variables by dividing be a measure of the amount

of substance (the molar volume, for example).

As well see next, certain quantities do not depend upon the path take by the

system; these are called state functions. Some thermodynamic state functionswe will be concerned with include:

U= internal energy

S = entropyH= enthalpy (classically, U + PV)

A = Helmholtz free enegy = U TS

G = Gibbs free energy = H TS

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Ch 21b - The First Law of Thermodynamics

23Feb2007

This law is, essentially, a statement of the conservation of energy. Suppose asystem is brought from state A to state B. The work done on the system during

this change is w, and the heat absorbed by the system is q. The first law states

that while w and q depend on the path taken by the system, their sum does not.

This sum is a state function, and is the internal energy. Mathematically:

dU = dq + dw

where the differentials are meant to emphasize infinitesimal changes.

dU, since it is path independent, is referred to as an exact differential, while dq

and dw are known as inexact differentials since their value depends upon the

path taken by the system. Cyclic processes bring the system back to its initial

state, and so for such processes the internal energy change is zero.

AB

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dU = 0

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Ch 21b - The Second Law of Thermodynamics

23Feb2007

The second law is a bit more abstract, and can be stated many ways. One is:There is a quantity S, called entropy, which is a state function. In an

irreversible process, the entropy of the system and its surroundings increases.

For a reversible process, the entropy of the system and its surroundings

remains constant. Mathematically:dS = dqrev/T

where the differentials are again meant to emphasize infinitesimal changes.

Reversible processes are those in which the driving force (a difference in P, T,

etc.) is infinitesimal. Any other change is called irreversible or spontaneous.

Reversible Irreversible

S = SA SB = dqrev/T or SA SB > dqirrev/T

Given the formulation above, the first and second laws can be

combined to yield the well known perfect gas equation:

dU = TdS PdV (heat + work)Page 5

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Ch 21b - The Third Law of Thermodynamics (Nernst Heat Theorem)

23Feb2007

The second law relates the infinitesimal change in entropy, an exact differential,to that in the infinitesimal change in the heat exchanged (which is inexact

since it depends on the path of the system) under isothermal conditions. The

integral needed to calculate the change in entropy, however, has an additive

constant associated with its calculation. The third law, which can be writtenin several forms, deals with this constant. One formulation is:

In any system in internal equilibrium undergoing an isothermal process

between two states, the entropy change of the process approaches zero as

the temperature of the system approaches zero. This enables us to calculatethe absolute entropy of a substance via the expressions

S S0 = dqrev/T and S0(T=0) = 0

where the integral runs from 0 to T. The restriction to states of internal

equilibrium is important. Frequently, during the approach to T= 0, a system

develops internal constraints that prevent the achievement of internal

equilibrium (glasses cannot turn into crystalline solids, for example, at low T).

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