thermodynamics - uniba.sk
TRANSCRIPT
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Thermodynamics
Classical thermod. Statistical thermod.
Early formulation: - transformation of heat to work in bulk matter
Current formulation:
- transformation of a given type of energy into another kind
of energy (energy balance of a thermod. process)
- direction of a spontaneous physicochemical processes
(equilibrium principle)
ENERGETICS, BIOENERGETICS
Methods of observation: empirical (experience, experiment)
mathematical - logical conclusion
Object of study: thermodynamic systems 1
Basic characteristics of classical thermodynamics:
- It is based on postulates (0th - 3rd law of thermodynamics),
which cannot be proven
- It is a phenomenological discipline (describes systems through
macroscopic properties and relationships between macroscopic
objects).
Does not require knowledge of the system structure. Does not
consider time-dependence of processes.
- Applies statistical considerations to systems composed of
large number of particles (disregards atomic or molecular
composition of systems)
- Individual variables describe states of gases, liquids or solids
and of ideal (reversible) processes 2
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Standard states in thermodynamics
Thermodynamics describes only changes of state functions -
does not define absolute values of physical quantities
Describes the state of the system with respect to a reference state, i.e.
standard state of thermodynamic functions (e.g. Ho, Go)
- gas in ideal state at pressure (p) of 101.32 kPa and standard temperature (T)
- liquid at p of 101.32 kPa and standard T
- solid (in most stable modification), at p = 101.32 kPa and standard T
- solution of a given substance at activity equal to 1, at p = 101.32 kPa
and standard T
Typical standard states:
Temperature: 0 oC 273,15 K STP = standard temperature and pressure
25 oC 298,15 K SATP = standard ambient temperature and
pressure3
Thermodynamic systems - components, phases
system
homogeneous heterogeneous
surrounding
Homogeneous sys. Heterogeneous sys. No. of phases No. of
components
Closed container full
of water1 - (l) 1- H2O
Closed container containing
water2 - (l, g) 1 - H2O
Closed container containing
water and ice3 - (s, l, g) 1 - H2O
Water solution of NaCl 1 - (l) 2 - H2O, NaCl
Oversaturated solution of NaCl 2 - (s, l) 2 - H2O, NaCl
Phase – homogeneous part of system, separated from other phases by boundaries at
which the physicochemical properties are discontinuous
surrounding surrounding
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Thermodynamic systems - according to boundary types
Open system - exchange of mass and energy
with the surrounding
Closed system - exchange of energy
Isolated system - no exchange
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Thermally isolated system = adiabatic system
No exchange of heat with its surrounding
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HeatExothermic process Endothermic process
releases energy in the form of heat into
surroundings
Consumes energy in the form of heat coming
from its surroundings
e.g. evaporation of watere.g. condensation, burning
In an adiabatic container
the temperature of system
undergoing exothermic
process will rise
To keep the temperature
constant in an isothermal
system undergoing exo-
thermic process the
produced heat must be
released to surroundings
In an adiabatic container
the temperature of system
undergoing endothermic
process will drop
To keep the temperature
constant in an isothermal
system undergoing endo-
thermic process the
consumed heat must be
supplied from surroundings7
Temperature t [oC, degree of Celsius]
Thermodynamic temperature T [Kelvin]:
T [K] = t [oC] + 273,15 K
Thermal equilibrium:
If:
T(A) = T(B)
T(B) = T(C)
then:
T(A) = T(C)
0th Law of Thermodynamics:
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Spontaneous flow of heat:
from an object of high temp. to low temp.
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Ideal gas: volume V, amount of substance n, temperature T
p = f (T, V, n)
p, T, V, n - state variables
p [Pa] 1 Pa = 1 N.m-2
mechanical equilibrium
Measurement of pressure:
manometer/barometer
h.g.p
h(tube of Torricelli )
Pressure:
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Ideal gas: Isothermic process, T = const.
(Robert Boyle, 1662)
p.V = const. (n, T = const.)
Isotherm
Boyle’s law:
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Ideal gas: Isobaric process, p = const.
Gay-Lussac’s law(J. Charles, 1787)
.constT
V n, p = const.
Isobar
Volume, V
Pre
ss
ure
, p
p = konst
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Ideal gas: Isochoric process, V = const.
.constT
p n, V = const.
Isochore
Volume, V
Pre
ssu
re,
p
V = konst
Gay-Lussac’s law(J. Charles, 1787)
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Ideal gas: State equation
nRTpV
R = 8.31447 JK-1mol-1 (molar gas constant)
[p, V, T] Volume, V
Pre
ssu
re,
p
V = konst
Volume, V
Pre
ss
ure
, p
p = konst
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Ideal gas: Avogadro’s principle
constnV p, T = const.
Molar volume: p
RTVm n = 1 mol
SATP: T = 298.15 K, p = 105 Pa Vm = 24.789 dm3mol-1
SATP – standard ambient temperature and pressure
STP: T = 273.15 K, p = 105 Pa Vm = 22.414 dm3mol-1
STP – standard temperature and pressure
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Heat and work - sign convention
All forms of energy (heat q, work w, entropy S, free energy G,
internal energy U, enthalpy H)
(energy) supplied to the system
+ -
(energy) leaving the system and
entering into surroundings
Categorization of quantities : everything that enters the system (+)
everything that leaves the system (-)
A B
q1=50J q3=80J
q2=20J
w=25Je.g.:
A: qA=q1+q2= 70 J
wA= -25 J
B: qB= -(q2+q3)= -100 J
wB= 25 J 15
Mechanical work of gas - expansion against constant external
pressure at pex = const.
ifex
V
V
ex VVpdVpw
f
i
Change of volume during expansion: if VVV
Vpw ex
Expansion V > 0, work done by the gas w < 0
Compresion V < 0, gas absorbs the work w > 0
work = force . trajectory
ds.Fdw
pressure = force/areaA
Fp ApF .
dVpdsApdw exex ..
Work done against external pressure pex:
16 ifex
V
V
ex VVpdVpw
f
i
ds.Fw
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Types of work
Type of work dw Characterization Units
Expansion
work
-pexdV pex is external pressure
dV is volume change
Pa.m3 = N.m = J
Surface
expansion.dA is surface tension
dA is area
Nm-1.m2 = N.m = J
Electric
work
E.dQ E is electrical potential
difference (voltage)
dQ is charge
V.C = J
Thermodynamic quantities:
Intensive: p, E, , T,... - are independent of the amount of substance
Extensive: V, A, Q, m, n,... - are proportional to the amount of subst.
(additive) 17
Expansion work - other types of work
Expansion work is associated with volume
change
pdVdwe
Non-expansion work (dwn) does not
involve change of the volume
occures also in biological systems.
Total work: ne dwdwdw
ne www 18
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State of the system
p1, T1
q1
q2
Steady state - non-equilibrium state - independent of the time
Metastable state - improper equilibrium
Thermodynamic equilibrium state = physical and chemical equilibrium
mechanic phase
System characterized by: state quantities (p, T, V, n, ...)
state functions (H, G, S, ...)
Change of state: 12 XXX X1 initial state
X2 final state 19
1 2
Change of state variable
Cyclic process X1 = X2
0dXX
Change of state variable is equal to zero.
1
2
X1,2
X2,1
0i
iX
01,22,1 XX
1
2
XA
XC
XB
CBA XXX
1
23
4
X1
X2
X3
X
41
321 XXXX
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Reversible and irreversible process
Irreversible process – all processes occurring in the nature
Reversible process – can be reversed at each stage,
– all stages during the process are considered
equilibrium states
(cannot be found in the real world)
T = const.
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Isothermal reversible expansion
Work of ideal gas during reversible isothermal expansion
nRTpV Ideal gas:
VpdVpw f
fV
iV
f .
V
nRTp
Irrev. work of gas:
i
f
fV
iVV
VnRT
V
dVnRT ln
The work of ideal gas during reversible isothermal expansion
displays maximum value
area under the isotherm > area under the isobare(irrev. work done against
same final pressure pf)
Isothermal rev. work: fV
iV
pdVw
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Work, energy and heatConservation of energy
James P. Joule (1849)Work: dsFw .
motion against an acting force F
Energy of system – ability to perform work
When the system changes its temperature
with respect to its surrounding the energy of
the system is transformed to heat.
Internal energy of system U – total potential and kinetic energy of
molecules forming the system
Change of internal energy: if UUU
Uf – final energy
Ui – initial energy1 J = 1 kg m2s-2
units [J]
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First Law of Thermodynamics
Internal energy of an isolated system is constant
wqU J.R. von Mayer (1842) and J.P. Joule (1849)
Defines the conservation of energy
Alternative definitions: the sum of all types of energy in a isolated system is constant;
perpetuum mobile cannot be constructed, etc.
- the law defines internal energy with help of observable quantities:
heat and work
-internal energy is a state variable, which depends
only on the state of the system (T, P, V, n, …,)
dwdqdU
pdVdwdwdwdwnen
Internal energy of 1 mol:
Um [J mol-1]
Differential form:
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Thermal capacity at V = const.
endwdwdqdwdqdU
Internal energy of an isolated system:
If the system does not do any work: 0e
dw 0ndw
dqdU (V = const., w = 0)
For observable changes: VqU
the heat qV (V = const.) describes the internal energy of the system
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V
VT
Uc
Thermal capacity at temperature T
is given by the tangent to the curve
U = f(T) for a given value of T.
Unit [J K-1]
Molar thermal capacity at V = const.:n
cc V
mV ,[J K-1 mol-1]
Specific thermal capacity at V = const.: m
cc V
sV , [J K-1g-1]
Thermal capacity at V = const.
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Calorimeter - thermal measurements of chemical processes
Adiabatic bomb
calorimeter
Differential scanning calorimeter
dTcH
T
T
exp2
1
,
TKq
K – constant of
the calorimeter
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Enthalpy H [J]
pVUH
Enthalpy is a state function
During izobaric process (p = const.) is the
enthalpy change equal to energy supplied as heat
dqdH
(p = const.)pqH
during small change: (p = const.)
VdppdVdUdH p = const. dp = 0 and U = q + w
pdVdUdH
VpUH 28
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Proof:
pqH
Overall change: U U + dU, V V + dV, p p + dp
pVUH
dpdVVdppdVpVdUU
dVVdppdUUdHH
))(()(
VdppdVdUHdHH
VdppdVdUdH
Internal energy: dwdqdU
VdppdVdwdqdH
System at equilibrium at p = const. performs expansion work: pdVdw
VdpdqdH p = const. dp = 0 dqdH 29
Thermal capacity at p = const.
p
pT
Hc
[J K-1]
Thermal capacity at temperature T
Is equal to the slope of the tangent to the curve
H = f(T) for given value of T.
Molar thermal capacity at p = const.:n
cc
p
mp ,
Specific thermal capacity at p = const.:m
cc
p
sp ,
[J K-1 mol-1]
[J K-1g-1]
For ideal gas: nRcc Vp
Measureble changes of T: TcH p
Infinitesimal changes of T: dTcdH p
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First Law of Thermodynamics at various conditions
wqU
Isobaric p = 0
Process
VpHU
Hq
VpqU
p
p
Isochoric V = 0 TcqU
Vpw
VV
0
Isotermic T = 0
wq
wq
TcU V
0
0
Adiabatic q = 0Tcw
wU
V
Thermaly isolated
container
Thermostat
Closed container
e.g. calorimeter
Cylinder with a piston at
constant atmospheric
pressure
System
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Second Law of Thermodynamics
Characterizes direction and possibility of accomplishing the process
Clausius (1850):
Heat cannot spontaneously transfer from a region of lower
temperature to a region of higher temperature
Kelvin (1851) and Planck (1891):
A machine working in a periodic cycle, which takes heat from a
reservoir and transforms it to an equivalent amount of work cannot
exist The direction of a spontaneous process is given by
the dispersion (dissipation) of energy.
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Molecular interpretation of irreversible processes
(ball on the floor)
a) a ball on the floor: random thermal motion of atoms
b) To make the ball spontaneously jump - random vibrational motions
of atoms must become organized (coordinated) – highly improbable33
Direction of spontaneous processes
Spontaneous processes tend to increase the random and chaotic
dispersion of energy of an isolated system
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Entropy S [J K-1]
Second law of thermodynamics defined with help of entropy:
First law of thermodynamics defines admissible changes in the system using
intenal energy (U)
Second law of thermodynamics identifies the direction of a spontaneous change
using entropy (S)
Entropy is a thermodynamic property that is a measure of the energy
not available for useful work in a thermodynamic process
Entropy of an isolated system remains constant or increases during a
spontaneous process 0 totSStot is the total entropy of the system and its surrounding
Entropy is an extensite quantity
Molar entropy: Sm [JK-1mol-1]
(Sm is an intensite quantity)
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Thermodynamic definition of entropy
Relationship between dissipated energy and its conversion to heat
T
dqdS rev
Change of entropy between states 1 and 2:
2
1T
dqS rev
Reversible process:
Irreversible – spontaneous process:T
dqdS
Cyclic process (unreal): 0 T
dqrev
e.g. Carnot cycle
Clausius inequality:T
dqdS
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Entropy - indicator of spontaneity of thermodynamic processes
OStot SSS SS – entropy change of the system
SO – entropy change of surroundings
System at equilibrium: 0 OS SS
Spontaneous process: 0 OS SS
Non-spontaneous process: 0 OS SS
Question: How to determine the entropy change of surroundings SO ?
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Entropy change of selected processes
a) Heating of a system from T1 to T2, at p = const.
1
2ln2
1
2
1
2
1T
Tc
T
dTc
T
dTc
T
dqS p
T
T
p
T
T
p
T
T
dTcdqdHp
Entropy of the system at T2:
1
2112 ln)()()(
T
TcTSSTSTS p
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b) During phase transition e.g. ice - liquid water, Ttr = 273 K, at p = const.
Both phases are at Ttr in equilibrium (reversible
process):
Hq tr
tr
trtr
T
HS
Exotermic phase transition: trH < 0 trS < 0
(freezing, vapor condensation )
Endotermic phase transition: trH > 0 trS > 0
(melting, evaporation)
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Thermal capacity & entropy of sample in the interval 0 – T
T
vT
p
v
vapvT
mT
p
m
mel
Tmp
T
dTgc
T
H
T
dTlc
T
H
T
dTscSTS
)()()()0()(
0
cp = f(T)
S = f(T)
phase transition
p = const.
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Third Law of Thermodynamics
At T 0 thermal motion of molecules and atoms is reduced to
minimum and particles are ordered to form perfect crystalline lattices
Nernst (1906) – zero theorem:
Entropy change of any physical or chemical process at absolute zero
(T = 0 K) is equal to zero.
0lim 0 ST
0lim 0 ST
Planck:
Entropy of each pure substance in crystalline, liquid state at the
absolute zero temperature (T = 0 K) is equal to zero
Lewis a Randall: … only for pure substance in perfect crystalline state
(not valid for overcooled liquids) 41
If the entropy of each element in their most stable state is taken equal
to zero, then all substances display entropy values > 0, which at
T = 0 K can reach the value of zero and which at T = 0 K is equal to
zero only for perfect crystals of pure substances and compounds.
Third law of thermodynamics:
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Questions:
• state equation of ideal gas, Boyle’s law, Gay-Lussac’s law
• thermodynamic systems, processes and variables
• zeroth law of thermodynamics
• first law of thermodynamics
• expansion work of gas
• enthalpy and thermal capacity
• direction of spontaneous processes
• entropy and second law of thermodynamics
• third law of thermodynamics
• entropy of a system at T