Thermodynamics - the
science that is concerned with energy, particularly ‘energy-in-transit’
in the forms of heat and work, and those properties of systems
that are related to energy.
Energy – the
ability to do work. All energy is relative! Energy-in-transit is not relative.
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 surroundings. The sum of
the system and the surroundings is the universe.
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 properties
of a material.
(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 = 2 + Ns - Np
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
[PVn] 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 Simple Statement: Heat and work are both forms of energy in
transit, and energy is always conserved. or
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 #1: Spontaneous fluxes always take place down
their corresponding potential gradients. or
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.