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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