Sect. 1 Basics of Thermodynamics

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Sect. 1 Basics of Thermodynamics

• The language of thermodynamics
• System the material in the portion of space to
  be analyzed
• Surroundings exterior environment
• Boundary A separator, real or imaginary,
  between system and surroundings

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Thermodynamic Systems

• Closed fixed mass (solid or fluid) within the
• Open (flow) A volume with partly solid
  boundaries and imaginary boundary sections
  through which fluid passes

surroundings
surroundings
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Example of a more complex system gas-cylinder
blowdown
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Boundary

• the boundary encloses the system
• Adiabatic (insulated) does not allow heat to pass
• Rigid cannot expand or contract (no work done)
• Isolated exchanges neither heat nor work with
  the surroundings (rigid and adiabatic)

Surroundings

• space outside the system boundary
• exchanges heat and work with system through
  boundary
• examples
• thermal reservoir exchanges heat with system
• work devices spring, piston, weight, atmosphere

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What does a system consist of?

• Components distinct chemical species
• single component pure substance
• 2. two components binary system
• a pure substance can become a binary system
• steam is a single component but at very high T,
  it dissociates into H2, OH, and O2 and becomes a
  two-component system (H and O)
• a binary system treated as a single component
• air is O2 N2, but at low T, is effectively a
  single component because composition doesnt
  change
• At very high temperatures, reaction produces NOx
• air is now a binary, with components N and
  O

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• Multicomponent system three or more components
• Steel is an alloy of Fe, Ni, and Cr this is a
  nonreacting ternary. The concentrations of the
  species are independent (but their atom fractions
  must add to unity)
• At low temperature, a mixture of H2, CO2 and O2
  is a nonreacting ternary at high temperature, it
  is a reactive ternary (H, C, and O) with many
  chemical reactions

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Phases regions of a system with uniform
properties

• phases are solid, liquid, or gas
• solids and liquids are collectively called
  condensed phases
• liquids and gases are collectively called fluid
  phases
• a gas phase can be called a vapor if it is
  condensible (e.g., H2O)
• a phase can contain one or more components

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Phases (cont)

• a homogeneous system consists of a single phase
• a heterogeneous system consists of two or more
  phases separated by sharp interfaces
• a system may contain more than one liquid or
  solid phases, but only one gas (vapor) phase
  examples
• solid liquid (e.g., ice and water)
• two solids (e.g., ?-Zr and ?-Zr)
• two solids and a gas (e.g., Fe, FeO, and O2)
• gas liquid (e.g., liquid water and steam)
• two immiscible liquids (e.g., oil and water)

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Thermodynamic properties single-component
(pure substance),

• characteristics that fix the condition of a
  system
• microscopic properties average of the quantum
  numbers of all atoms or molecules in a system
  statistical thermodynamics
• macroscopic properties (also called state
  variables) a few characteristics that determine
  the measurable gross condition of the system
  classical thermodynamics

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Classification of thermodynamic properties (for
a pure or 1-component substance)

• Fundamental p,T, V, U, S
• Auxiliary (derived from fundamental) H, F, G
• Absolute p, T, v, s, CP, CV
• Relative (to a reference state) U, H, F, G
• Extensive (? amount) V, S, U, H, F, G
• Intensive p, T (v, u, s, h, f, g)
• Derivative CP, CV, a, b

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fundamental macroscopic properties

• pressure (p) momentum transferred to walls by
  molecular impacts
• temperature (T) molecular speeds (gas) or
  amplitudes of atomic vibrations (solids)
• volume (V)
• internal energy (U) kinetic and potential
  energy contained in molecules or atoms
• entropy (S) measure of the degree of order of a
  system (disorder high S)

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Auxiliary properties

• enthalpy H ? U pV
• - like internal energy, but automatically
  accounts for pV work
• - ?H (change in enthalpy) is the heat added in a
  constant-p process
• - for an open (flow) system, H replaces U in the
  1st Law

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Auxiliary properties Free Energies

• Helmholz free energy F ? U TS - F is the
  link between statistical and classical
  thermodynamics (F is rarely used in purely
  classical approach)
• Gibbs free energy G ?? H TS
• - G is the criterion of equilibrium in chemical
  reactions
• - DG is the maximum work done (or needed) in a
  flow process.

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Absolute and relative properties

• p, T, V, and S are absolute zero values are
  unique
• - absolute zero temperature 0 K
• - The absolute zeros of p and V are obvious
• - CP and CV are derivatives of relative
  properties
• - The absolute value of S comes from the 3rd
  Law The entropy of a solid is zero at 0 K.
  (all substances are solid at
  this temperature)
• U, H, F, G are relative i.e., they must be
  assigned a zero value at an arbitrary reference
  state (the same state for all four)

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Extensive and Intensive properties

• Extensive value proportional to amount in
  system V, U, S, H, F, G
• Intensive value independent of the amount of
  material p, T
• For a one-component system (pure substance)
  extensive properties can be made intensive by
  dividing by the amount (n moles of substance)
• - v V/n v molar volume, or
  reciprocal of the
  molar density
• - u U/n s S/n h H/n g G/n

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Derivative Properties

• Specific heats (heat capacities)
• CP (?h/?T)P - constant-pressure
• CV (?u/?T)V - constant-volume
• Coefficients of expansion
• a (1/v)(?v/?T)P - thermal expansion
• a(Hg) used for mercury thermometer
• b -(1/v)(?v/?p)T - compressibility

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Units of thermodynamic properties(SI, or metric)

• pressure Pascal(Pa) Newton(N)/m2 10-5 atm
  temperature Kelvins (K) or degrees Celsius oC
  K 273 (strictly, not SI)
• volume cubic meters (m3) length in meters (m)
• U, H, F, G Joules(J or kJ), calorie or kcal also
  used
• - 1 cal 4.184 J 1 kcal 4.184 kJ
• KE ½mv2 kg-m2/s2 but from F ma, N kg-m/s2
• ? kg-m2/s2 N-m J

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Thermodynamic State of a pure substance

• all properties fixed if any two are specified.
  (why 2? see later)
• To know all properties, two Equations of State
  (EOS) are needed
• - v(p,T) volumetric EOS
• - CP(T,p) or CV(T,v) thermal (EOS) -
  fixes s, u, h, g (with specification of a ref.
  state)

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Heat (Q)

• Energy exchanged between system and surroundings
  (reservoirs) due to a DT
• Mechanisms (not thermodynamic)
• - conduction molecular motion
• - convection bulk fluid movement
• - radiation electromagnetic fields
• Heat is not a thermodynamic property it causes
  changes in them

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Work (W)

• Expansion (pV ) W F?x (F/A)(A?x) p?V
• Shaft rotation of a shaft by a moving fluid
• Electrical flow of electrons down a potential
  gradient
• External all F?x except p?V
• why? p?V is often not useful work just
  pushing back or being pushed by the surrounding
  atmosphere
• Work is not a thermodynamic property, but can
  change them
• All forms of work are theoretically
  interconvertible

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Thermodynamic Processes

• Cannot infer Q from this diagram
• Path depends on how T varies with V.

• -Process - change in p-V-T state of system due to
  exchange of heat and/or work with the
  surroundings.
• - Plot process path on a
• pressure-volume graph
• state of system at 2 is
• independent of path (A or B)
• but, Q and W are different for each path

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ISO processes

• In most processes, one property is constant

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Reversible Processes

• Internal in the system
• External in the surroundings
• Work done by the system is the same as the work
  done on the surroundings
• For the same initial and final states, work done
  reversibly is always gt work done irreversibly
• Requirements of reversibility
• - very slow moves through equilibrium states
  
• - in fluids, no turbulence
• - no friction
• - infinitesimal T Tsurr for heat p psurr
  for work
• -

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Example Reversible Isothermal compression of an
ideal gas

• add small weights (total mass m) so that descent
  of
• piston is gentle remove heat with very small T -
  Tsurr
• This is also Wsurr, the work done by the
  surroundings

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Irreversible version

• add single block of mass m rapid descent
• violent bouncing of piston until final state
  reached
• Cannot integrate pdV

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Work to compress irreversibly

• the work done by the surroundings can be
  calculated
• Wsurr psurr(Vo-Vf) mg (Vo-Vf)/A
• Force balance on final state pf psurr mg/A
• Combine
• Wsurr - pf (Vo-Vf) - pfVf(Vo/Vf - 1) -nRT
  (Vo/Vf - 1)
• For Vo/Vf 3
• The surroundings do less work in the reversible
  than in the irreversible process

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Internal equilibrium (system)

• Single phase
• - no change of pressure, temperature or
  composition with time (mechanical, thermal
  chem. equilibrium)
• - no gradients of any properties, except at
  interfaces between phases
• Multiphase - each phase must have
• - same temperature (thermal equilibrium)
• - same pressure (mechanical equilibrium)
• - same chemical potential (chemical equilibrium)

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External Equilibrium(between system and
surroundings)

• Both have the same pressure (unless the boundary
  is rigid)
• Both have the same temperature (unless the
  boundary is adiabatic)
• No work can be performed by or on the system (no
  Dp, DT or Dm)

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Constraints and equilibrium

• Constraining a system means fixing two of its
  properties
• If U and V are fixed (isolated system),
  equilibrium occurs when the entropy is a maximum
  (mainly of theoretical importance)
• If p and T are fixed, equilibrium occurs when the
  Gibbs free energy is a minimum (useful for phase
  equilibrium and chemical equilibrium)

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The First Law of Thermodynamics

• Cannot be derived from any fundamental principle
  (it is one)
• Has never failed an experimental test in 150
  years
• Comes in two versions
• - within a system the 1st law
• - between system and surroundings or two
  systems Law of Conservation of Energy

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1st Law

• relates changes in system energy to heat and
  work
• ?U ?(PE) ?(KE) Q W WS Wel
• U internal energy
• PE potential energy
• KE kinetic energy
• Q heat (positive if added to the system)
• W expansion (pV) work if done by the system
• WS shaft work (rotation of a shaft)
• Wel electrical work (charging a battery)
• Heat and work are equivalent in the 1st law
• Even though Q and W are path-dependent, ?U is not

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Conservation of Energy

• Heat and work are exchanged between the system
  and the surroundings
• DUsys (Q W)sys
• DUsurr -(Q W)surr
• Add the 1st Laws for system surroundings
• DUsys DUsurr 0
• This is the Law of Conservation of Energy

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Where the 1st Law is inadequate

• Consider an isolated system consisting of two
  rigid subsystems of different temperatures that
  communicate thermally
• Energy conservation and the 1st Law yield
• ?U1 ?U2 Q1 Q2 0 or Q1 - Q2
• Either Q1 or Q2 must be negative (i.e., one of
  the two arrows must be reversed) the 1st Law
  cannot tell which one, but the 2nd Law can.

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The Second Law of Thermodynamics

• The 2nd Law was discovered by Clausius from
  numerous observations showing that if a process
  is reversible, is
  path-independent.
• Any quantity whose change is independent of the
  path must be a thermodynamic property as in the
  1st Law, where Q W is path-independent
• Clausius called the property entropy, with the
  symbol S

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Irreversible processes

• For irreversible processes, the equality no
  longer holds. Instead
• In irreversible processes, entropy is created!
• Other forms of the 2nd Law
• dS ?

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law of entropy production

• Entropy production is to the 2nd Law as
• energy conservation is to the 1st Law
• add 2nd Law for system and surroundings
  (TsurrgtTsys)
• entropy can be produced but never
  destroyed

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The direction of heat flow revisited

• begin with ?S1 ?S2 gt 0
• but DS1 Q1/T1 and DS2 Q2/T2 (heat flow to and
  from reservoirs is reversible)
• T1 ? T2, is the source of irreversiblity
• Q1/T1 Q2/T2 gt 0 from 1st Law Q1
  -Q2
• 
  
• If T1gtT2, then Q2 gt0
• and Q1lt0

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How to calculate system entropy change for an
irreversible process

• Example doubling the volume of an ideal gas
• in an isolated system (DU 0)
• Irreversible version
• initial state (To) final
  state(To)
• Boltzmann eqn SnNAvklnW DSnRln(Wf/Wo) nRln2

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• Reversible version

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• DU 0 for the reversible process as well
• from the 1st Law, Q W
• work can be calculated for the reversible
  process only
• From the 2nd Law
• DS Q/T nRln(Vf/Vo) nRln2
• Since entropy is a thermodynamic property, the
  path used to compute it is immaterial
• ?S computed for the reversible process is the
  same as the ?S for the irreversible process
• (but, work was done in reversible process)

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Entropy, Free Energy and Equilibrium

• for a closed system du ?q - ?w(PV) -?wext

For reversible process Tds pdv

• Electrical (battery)
• Chemical (ATP?muscle)

du Tds pdv - ?wext
d small increment of heat or work d small
increment of a thermodynamic property

• isolated system, dv du 0

• Equilibrium system cannot perform external work,
  or dwext 0

s
equilibrium state
State of system
At equilibrium with u v constant the entropy is
a maximum
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Thermal equilibration of identical solids
energy conservation

T1
T2
Tf
Tf
Q
DUTot?U1?U2 0
CV(Tf T1) CV(Tf T2) 0
Tf ½(T1 T2)
?STot ?S1 ?S2
Eliminate Tf
T2/T1 ?STot/CV 0.9 0.0028
1.0 0 1.1 0.0023
Thermal equilibration results in an increase in
the entropy of the isolated system
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Enthalpy
h ? u pv ? dh du pdv vdp ? use du
equation
dh Tds vdp - ?Wext
Helmholz free energy
f ? u Ts ? df du Tds sdT ? use du
equation
df - pdv sdT - ?Wext
Gibbs free energy
g ? h Ts ? dg dh Tds sdT ? use dh
equation
dg vdp sdT - ?Wext
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Neglecting external work
du Tds pdv

• These were derived assuming reversible ?q and
  ?W(pv)

dh Tds vdp
df - pdv sdT

• However, since they involve only state functions
  (properties), they are valid for any process

dg vdp sdT

• Collectively, they are called
• Fundamental differentials, or
• Tds equations (first two), or
• Gibbs equations

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Equilibrium at constant T and p
dg vdp sdT - ?Wext
with dT dp 0

• Reversible non-pv work at constant p and T

• System is at equilibrium when dwext 0

equilibrium state
g
State of system
At equilibrium with p T constant the Gibbs free
energy is a minimum
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The Phase Rule

• Fixes how many properties can be varied for a
  given number of components (C) and phases (P)
• The allowable variable properties are called
  degrees of freedom (f)
• Single component (C 1) 1 phase (P 1) f 2
• Single component (C 1) 2 phases (P 2) f 1
• e.g. the vapor pressure of a condensed phase
  F(T)
• Single component (C 1) 3 phases (P 3) f 0
• e.g. the triple point where gas, liquid solid
  coexist
• Two components (C 2) 3 phases (P 3) ? 1
• e.g. a metal, its oxide and O2 gas at each T,
  there is a unique at which M and MOx
  coexist

f C 2 P - Nrxn
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