__ __

__ __

__ __

** Thermodynamics** - the
science that is concerned with

** Energy** – the
ability to do work.

**Three kinds of energy**:

(1) __potential__ - energy due to *relative*
position,

(2) __kinetic__
- energy due to *relative* velocity,

(3) __internal__
- the sum of all potential and kinetic energies of constituent parts
[atoms, molecules, etc.] of a system.

**Two kinds of ‘energy-in-transit’**:

(1) __heat__ – energy transferred between system and
surroundings because of a temperature difference, or gradient.

(2) __work__ - energy transferred between system and
surroundings because of a pressure difference, or gradient.

** **

** **

** Thermodynamic System** – just “the thing” that we are talking about! Everything else is called the

**Three
kinds of systems**:

(1) __closed system__ – a fixed quantity of material;
energy can cross the system boundaries but mass can not.

(2) __open system__ – a particular region of space; both
mass and energy may cross the system boundaries.

(3) __isolated system__ (not an important concept) –
neither energy nor mass may cross the system boundaries.

In elementary thermodynamics all systems consist only of
atoms and molecules where the net electric charge of the system is zero. In addition, all electrical and magnetic and
surface forces are generally neglected.

**Two kinds of materials**:

(1) __pure materials__ - composed of only one molecular
species, and

(2) __mixtures__ - composed of two or more molecular
species.

__ideal mixtures__ - mixtures where the volume and
enthalpy of the mixture are simply the sums of the volumes and enthalpies of
the pure components at the temperature and pressure of the mixture. Elementary thermodynamics deals only with
ideal mixtures. Advanced thermodynamics
is concerned with non-ideal mixtures, in phase equilibrium and reaction
equilibrium.

**Four basic concepts of materials:**

(1) __Quantity____ __

(a) mass (or
weight in a known gravitational field)

(b) number of
objects (one gram mole = 6.025 x 10^23 objects)

__mean-molar-mass__ (molecular weight or atomic weight) is
the mass of one mole of a particular collection of objects, and is the constant
which allow conversion between these two measures of quantity.

(2) __Composition____ of a mixture__

(a) __fraction__
- quantity of a particular species per unit quantity of the mixture.

(b) __concentration__
- quantity of a particular species per unit volume of the mixture.

(3) ** Phase** - a homogeneous quantity of
material, characterized throughout by a single set of thermodynamic properties.

(a) __solids__ - materials which are
capable of resisting shear stresses.

(b) __fluids__ - materials which exhibit
continuous deformation under shear stress.

(c) __liquids__ - fluids which can
conform to their containers without occupying them completely.

(d) __gases__ - fluids which conform to
and completely occupy their containers.

(e) __vapors__ - gases at temperatures
less than their critical temperature.

__quality__ - ratio of quantity of vapor to the
total quantity of material [vapor & liquid] or [vapor & solid] in a
system.

(4) ** State** - defined by the

(a) __subcooled
liquid__ (or __compressed liquid__) - a liquid at a temperature below its
saturation temperature or at a pressure above its saturation pressure.

(b) __superheated
vapor__ - a vapor at a temperature above its saturation temperature or at a
pressure below its saturation pressure.

(c) __saturated__
- if two or more phases exist within a system at **equilibrium**, the system
is said to be saturated and all phases present are saturated. In particular, if vapor and liquid phases
are both present within a system, the vapor is said to be **saturated vapor**
and the liquid is said to be **saturated liquid**. Similarly, if two liquid phases exist within a system at
equilibrium, both liquid phases are saturated.

__saturation pressure__ (or __vapor pressure__) - the
pressure at which a phase change will take place at a given temperature.

__saturation temperature__ - the temperature at
which a phase change will take place at a given pressure.

__critical point__ - that state of a saturated system
where the liquid and vapor phases become indistinguishable. The properties of a material at its critical
point are the same for both vapor and liquid phases.

__equilibrium__ - the condition of a system in which
no net change in the properties of the system occur with time. A closed system is usually implied.

__[steady state__ - no accumulations of matter or energy
occur within the system. An open system
is implied.]

** Thermodynamic
Properties** - any quantity that depends only on the state of a material
and is independent of the process by which a material arrives at a given state.

__Properties of a System__ - the average or
homogeneous properties of a system at equilibrium.

**Two kinds of properties**:

(1) __intensive__ - independent of the quantity of
material [T, P, Cp and Cv], and all specific and molar properties.

(2) __extensive__ - directly proportional to the quantity
of material [V, S, U, H, etc.].

__Pseudointensive properties__ - extensive properties
expressed per unit quantity of material [v, s, u, h, etc.].

**Two kinds of pseudointensive properties**:

(1) __specific properties__ - expressed on a unit mass
basis, and

(2) __molar properties__ - expressed on a unit mole
basis.

**Five basic thermodynamic properties:**

(1) __temperature [T]__ (thermal potential) - a measure
of the relative hotness or coldness of a material.

(2) __pressure [P]__ (mechanical potential) - the normal
(perpendicular) component of force per unit area.

(3) __volume [V]__ (mechanical displacement) - the
quantity of space possessed by a material.

(4) __entropy [S]__ (thermal displacement) - the quantity
of disorder possessed by a material.

(5) __internal energy [U]__ - the energy of a material
which is due to the kinetic and potential energies of its constituent parts
(atoms and molecules, usually).

**Two secondary thermodynamic properties**:

(1) __enthalpy [H]__ - internal energy plus the
pressure-volume product.

(2) __heat capacity [Cp or Cv]__ (specific heat) - the
amount of energy required to increase the temperature of one unit quantity of
material by one degree, under specific conditions.

(a)
constant pressure Cp = dh/dT

(b)
constant volume Cv
= du/dT

Unlike gases, liquids and solids are nearly incompressible,
and it is almost impossible to change their temperature while holding their
volumes constant. The __specific heats__
of liquids and solids almost always imply their constant pressure heat capacity
(usually on a unit mass basis), so that, in general, for liquids and solids we
used Cp.

** Gibbs Phase Rule**:

**F** - __degrees of freedom__ of the
system = the number of *independent*,

*intensive* __thermodynamic variables__ (properties or
compositions) which

must be specified
to fix the *intensive* state of the
system,

**Ns** - number of molecular species within
the system, and

**Np** - the number of phases within the
system.

The thermodynamic variables specified as degrees of freedom
are normally temperature, pressure and compositions (mole fractions) of the
phases. Note that only [Ns - 1]
compositions of each phase are *independent*. To fix the *extensive* state of the system, an additional *extensive* variable must be specified (i.e. total moles of the
system).

__process__ - any succession of events.

__chemical process__ - a chemical or physical operation, or
series of operations, which transforms raw materials into products.

__thermodynamic process__ - the path of succession
of states through which the system passes in moving from an initial state to a
final state.

__polytropic process__ - a thermodynamic process for which
[PV^{n}] is constant. These
processes are usually associated only to systems for which the ideal gas
assumption holds.

**Four special polytropic
processes**:

(1) __isobaric__
- - - - - - - constant pressure [n
= 0]

(2) __isothermal__
- - - - - - constant temperature[n = 1]

(3) __isentropic__
- - - - - - constant entropy [n
= gamma,(Cp/Cv)]

(4) __isochoric__ (__isometric__) - constant volume [n = infinity]

**Two other important processes**:

(1) __adiabatic__ - no heat transfer.

(2) __isenthalpic__ - constant enthalpy. This is the same as isothermal for an ideal
gas system.

__reversible process__ – an *idealized* process in which
the deviation from thermodynamic equilibrium is infinitesimal at any particular
instant during the process. All of the
states through which a system passes during a reversible process may be
considered to be equilibrium states.
This is an *idealized* situation that would require infinite time and/or
equipment size to be realized. The
concept of a __reversible process__ serves to set a maximum for the
efficiency of a given process. Note
that an *isentropic* process is an adiabatic-*reversible* process, so that real *isentropic* processes are not
possible.

__thermodynamic cycle__ - a process for which the final and
initial states are the same.

**Four common ‘ idealized’ thermodynamic cycles**:

(1) __Carnot cycle__
- isothermal and isentropic compressions followed by

isothermal and isentropic expansions.

(2) __Rankine cycle__ - isobaric and isentropic compressions followed by

isobaric and isentropic expansions.

(3) __Otto cycle__
- isentropic and isochoric
compressions followed by

isentropic and isochoric expansions.

(4) __Diesel cycle__
- isentropic compression followed by isobaric,

isentropic and isochoric expansions

Data, such as properties of pure materials, is generally
acquired by experimentation and can be presented in three fundamentally
different forms:

(1) **Tables**
[i.e. the steam tables]

(2) **Graphs**
[i.e. a T-s or P-h diagrams]

(3) **Equations** [i.e. the ideal gas equation]

Each of these forms of presentation has advantages and
disadvantages.

(1) __Tables__ are precise but discontinuous, so that
interpolation is often required. In
addition, they can be bulky and can be difficult to use when implicit variables
are specified. They also can require
large amounts of data storage when used with computer programs.

(2) __Graphs__ are continuous in their explicit variables
but suffer loss of precision when they are of convenient size. In addition, they are discontinuous for
implicit variables, so that imprecise visual interpolation is often
required. They also suffer in
readability as the number of implicit variables displayed increases above three
or four. Although they can give an
excellent overall "feel" for the data, they are virtually useless for
computer purposes.

(3) __Equations__ are in many ways the best form of
presentation for data. They allow
mathematical manipulation, are easy to use with computer programs, and are as precise
as the data used to generate their constants.
However, equations that accurately represent significantly large ranges
of data can be very complex and usually employ a number of constant terms. Complex equations are usually difficult to
solve for their implicit variables and often require trial and error procedures
in their use. They are most suited for
use in computer programs.

__Thermodynamic
Laws__

A physical law is a simple statement of an observable
physical phenomenon that has no underlying, more-basic reason for being except
that the most accurate observations have always proved it to be true.

**Laws
of Thermodynamics**

** Zeroth**:
Two bodies in thermal equilibrium with a third body are in thermal
equilibrium with each other. (This ?Law?
simply states that ‘thermometers work’.)

** First**:

__A Classical
Statement__: During any cyclic process on a closed system the cyclic integral
of heat is always equal to the cyclic integral of work.

** Second**:

__Simple
Statement #2__: Heat and work are both forms of energy in transit, but they
are not qualitatively equal forms of energy because work can always be
converted entirely into heat, but heat can never be converted entirely into
work. **or**

__Kelvin-Plank
Statement__: It is impossible to
construct a device which operates in a cycle and produces no effect other than
the raising of a weight and the exchange of heat with a single reservoir. **or**

__Clausius
Statement__: It is impossible to
construct a device which operates in a cycle and produces no effect other than
the transfer of heat from a cooler body to a hotter body.

Albert Einstein considered the Second Law of Thermodynamics
to be the **only** real physical law.

** Third**:
The absolute entropy of a pure, crystalline material at a temperature of
absolute zero is zero. (This ?Law? is
the second half of the definition of entropy.)

**Other
Laws of Importance in Thermodynamics**

__Conservation of Matter__: Matter can be neither created nor destroyed
but only changed from one form to another.
Note that Albert Einstein showed that matter could be ‘destroyed’ by
converting it into energy.

__Joule's ?Law?__:
The internal energy of an ideal gas is a function of temperature only.

__Avagadro's ?Law?__:
Equal volumes of different ideal gases at the same temperature and
pressure contain the same number of molecules.