Polymer Thermodynamics Lecture 0331 L 337 2. First and Second Law of Thermodynamics

Prof. Dr. rer. nat. habil. S. Enders Faculty III for Process Science Institute of Chemical Engineering Department of Thermodynamics

Lecture

Polymer Thermodynamics 0331 L 337 2. First and Second Law of Thermodynamics Polymer Thermodynamics 2 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics

Case a) Change of state for copper cube Copper cup has no possibility to exchange heat with the surrounding. The temperature may be 298K and kept constant. The system copper is in

state 1 characterized with temperature T1 and pressure P0 (and with mass m=8.96g).

Case b) Using Bunsen burner we heat-up the copper for a short time. The metal takes the heat via his surface. The heat will be distributed on the whole phase very rapidly. The surrounding (in this case the Bunsen burner) gives a certain amount heat, Q, to the system (in this case the copper). The

related heat can be calculated using Q=CCu⋅m⋅∆T.

Case c) The copper cube is again thermic isolated and his temperature is now

310 K. The system is now in the state 2 characterized with temperature T2, where temperature T2 is higher than temperature T1. The state 2 has more energy, because heat is added to the system. Polymer Thermodynamics 3 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics

In order to distinguish clearly between the total energy (internal, potential and kinetic) of a system and energy, which can be exchanged with the surrounding, we introduce the term internal energy U. The internal energy can not be measured directly, only its change can be measured via accurate measurements of the exchanged energy.

The change of internal energy is equal to

9 the difference in energy ∆U (internal energy of Copper in state 2 – internal energy of Copper in state 1) 9 the sum of energies exchanged with the surrounding during the change of state

In our example we can measure the internal energy measuring the heat Q during the change of state. Polymer Thermodynamics 4 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics

The equivalence of change in internal energy on one side and the change in heat and work on the other side has to be reality, because the law of energy conservation.

before afterward

± heat J system system P2,V2,T2,n P1,V1,T1,n ± work W

change of state state 1 state 2 Polymer Thermodynamics 5 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics dU= dW+ dQ

The exchanged amount of work and heat of a system is identical to the change of internal energy of the system.

or: A Perpetual motion of the first kind do not exist..

route 1

T2, P2, T1, P1, V1, U1 V2, U2 route 2 Polymer Thermodynamics 6 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics dU = dW+ dQ

UfTVnnn= (, ,12 , ..)i caloric equation of state exact differential ⎛⎞∂∂∂UUU ⎛⎞ ⎛⎞ dU=++⎜⎟ dT ⎜⎟ dV⎜⎟ dn1 ⎝⎠∂∂∂TVnVn,, ⎝⎠ Tn 1 jj⎝⎠TVn,,j≠1

⎛⎞∂∂UU⎛⎞ can be estimated +++⎜⎟ dn2 … ⎜⎟ dni only via the second ∂∂nn2 i law of thermodynamic ⎝⎠TVn,,j≠2 ⎝⎠TVn,,ji≠

⎛⎞∂∂UU ⎛⎞ ⎛⎞ ∂ U dU=++⎜⎟ dT ⎜⎟ dV∑ ⎜⎟ dni ⎝⎠∂∂TVVn,, ⎝⎠ Tn i ∂ ni jj⎝⎠TVn,,ji≠ Polymer Thermodynamics 7 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics

⎛⎞∂U ⎡⎤JJ ⎡ ⎤ CV = ⎜⎟ Cc ∂T VV⎢⎥ ⎢ ⎥ ⎝⎠Vn, j ⎣⎦K ⎣molK ⎦

The heat capacity, cV, is the heat which is necessary to warming one mol of the substance by 1K under isochore conditions.

T=298.15K substance c [J/(mol K)] V P=0.101 MPa water (liquid) 75.15 water (vapor) 33.56 acetone 125 Polymer Thermodynamics 8 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics dU= dW+=−+ dQ PdV dQ for isochoric processes: dU= dQ caloric equation of state Lots of processes are going on at constant pressure (i.e. atmospheric pressure). introduction of a new thermodynamic function

HUPV= + H = enthalpy = function of state dH= dU++ PdV VdP dH=− PdV ++dQ PdV +VdP dH=+ dQ VdP caloric equation of state for isobaric processes: dH= dQ Polymer Thermodynamics 9 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics

HfTPnnn= (, ,12 , ..)i caloric equation of state exact differential ⎛⎞∂∂∂HHH ⎛⎞ ⎛⎞ dH=++⎜⎟ dT ⎜⎟ dP⎜⎟ dn1 ⎝⎠∂∂∂TPnPn,, ⎝⎠ Tn 1 jj⎝⎠TPn,,j≠1 ⎛⎞∂∂HH⎛⎞ can be estimated +++⎜⎟ dn2 … ⎜⎟ dni only with the second ∂∂nn2 i law of thermodynamic ⎝⎠TPn,,j≠2 ⎝⎠TPn,,ji≠

⎛⎞∂∂HH ⎛⎞ ⎛⎞ ∂ H dH=++⎜⎟ dT ⎜⎟ dP∑⎜⎟ dni ⎝⎠∂∂TPPn,, ⎝⎠ Tn i ∂ ni jj⎝⎠TPn,,ji≠ Polymer Thermodynamics 10 2. First and Second Law of Thermodynamics 2.1. First Law of Thermodynamics

⎡ JJ⎤⎡ ⎤ ⎛⎞∂H Cc CP = ⎜⎟ PP⎢ ⎥⎢ ⎥ ∂T ⎣ K ⎦⎣molK ⎦ ⎝⎠P,n j

The heat capacity, cP, is the heat which is necessary to warm one mol of the substance by 1K under isobaric conditions.

substance cP [J/(mol K)]

ammonia 35.52 T=298.15K P=0.101 MPa bromine 75.71

lead sulfate 104.3 Polymer Thermodynamics 11 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

The first law of thermodynamics does not say anything in which direction the process takes please. The first law of thermodynamics leads only to dU= dW+ dQ

Marine propulsion can be established according the first law of thermodynamics by constructing an engine that use heat of the ocean and transformed this heat completely into work. The work goes back to the ocean via friction.

W. Ostwald: Perpetual motion of second kind

Such a ship does not exist. Why ??? Polymer Thermodynamics 12 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

N2 O2

Two different gases do not demixing voluntary, although it will be possible for energetic reasons. Air

Why ???

N2 O2 Polymer Thermodynamics 13 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

T =318 K T1=298 K 2

dQ1 ?dQ2 ? T3 ? Polymer Thermodynamics 14 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

detonating gas reaction

At 600°C the following reaction will be run spontaneously:

2 H2+O2 → 2 H2O

Accompaniment: noisy bang, risk for explosion

Nobody has observed that water vapor decomposes in his elements (oxygen and hydrogen) at 600°C. Polymer Thermodynamics 15 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Max Planck (1897)

It is impossible for every device that operates on a cycle to receive heat from a single reservoir and produce a net amount of work.

There is no perpetual motion of the second kind. This device uses the heat of a reservoir and transfer it into mechanical energy.

All real processes in nature are irreversible processes.

Reversible process is a process or operation of a system or a devise that a net reverse in operation will accomplished the converse of the original functions. For a reversible process the net change at each stage of the system and the surrounding is zero and it can be reversed at each stage.

Reversible processes are idealized limiting cases of real processes and they are infinity slowly, because all changes of state are differential small. All processes going on with finite speed are irreversible (all real processes). Polymer Thermodynamics 16 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

All real processes in nature are irreversible processes.

Example: Evaporation of superheated water (i.e. at 110°C) = irreversible Process thermometer notional fragmentation in different reversible processes cooling water

1. Cooling of water to 100°C 2. Evaporation in equilibrium column 3. Heating of water vapor to 110°C

distillate distillation flask Polymer Thermodynamics 17 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Carnot Cycle (1824) pressure pressure

volume volume isothermal adiabatic expansion expansion ↑heat at T1 isolator pressure pressure

volume volume adiabatic isothermal compression compression isolator ↓ heat at T2 Polymer Thermodynamics 18 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Carnot Cycle with ideal gas A → B Isothermal expansion

⎛⎞VV22 ⎛⎞ isotherm WAB=− nRT11ln⎜⎟ Q AB = nRT ln ⎜⎟ ⎝⎠VV11 ⎝⎠ pressure isotherm B → C adiabatic expansion

WCTTQBC=− V( 21) BC =0 volume

C → D isothermal compression

⎛⎞VV44 ⎛⎞ WnRTCD=−22ln⎜⎟ QnRT CD = ln ⎜⎟ ⎝⎠VV33 ⎝⎠ D → A adiabatic compression

WCTTQDA= v( 21−=) DA 0 S.N.L Carnot (1796-1832) Polymer Thermodynamics 19 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Carnot Cycle with ideal gas

Law of Poisson

isotherm PV κ = constant pressure isotherm ()−1 ⎛⎞VV⎛⎞ TV κ =→=constant ⎜⎟41⎜⎟ ⎝⎠VV32⎝⎠ volume

WW=+++AB W BC W CD W DA ⎡⎤ ⎛⎞VV24⎛⎞ ⎛ V2 ⎞ Wn=+→R ⎢⎥TT1 ln⎜⎟2 ln ⎜⎟ WnRT=−()1 T2 ln ⎜⎟ ⎣ ⎝⎠V1 ⎝⎠V3 ⎦ ⎝ V1 ⎠ Polymer Thermodynamics 20 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

Carnot Cycle with ideal gas

isotherm benefit pressure efficiency = isotherm effort work done volume ==η used heat For the whole cycle is valid: dU= 0 →− W = Q

used heat== QABCD supplied heat Q W Q QQ+ Q η ===ABCDCD =+1 QQABABAB Q Q AB Polymer Thermodynamics 21 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Carnot Cycle with ideal gas

⎛⎞V2 WnRTT=−()12ln ⎜⎟ ⎝⎠V1 isotherm η = efficiency pressure isotherm supplied head = QAB W Q η ==+1 CD volume QQAB AB

⎛⎞V nR() T− T ln 2 QQTQ 12 ⎜⎟ CD=−2 CD =− AB ⎝⎠V1 ()TT12− T2 η ===−1 QTAB 12TT1 ⎛⎞V TT nRT ln 2 11 Q Q 1 ⎜⎟ CD +=AB 0 ⎝⎠V1 T21T The efficiency depends only on temperature difference. Polymer Thermodynamics 22 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Carnot Cycle with ideal gas Q Q CD + AB = 0 isotherm TT21 dQrev pressure Clausius (1854) dS = isotherm T S = entropy ⎡ ⎤ volume ⎡⎤JJ Ss⎢⎥ ⎢ ⎥ ⎣⎦KmolK⎣ ⎦ Rudolf Julius Emanuel Clausius (1822 – 1888), was a German physicist and mathematician and is considered one of the central founders of the science of thermodynamics. His most important paper, on the mechanical theory of heat, published in 1850, first stated the basic ideas of the second law of thermodynamics. In 1854 he introduced the concept of entropy. The entropy, denoted by the symbol S, is a state function. Polymer Thermodynamics 23 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Carnot Cycle with ideal gas

1) isothermal expansion: dS=dQAB/T1 2) adiabatic expansion: dS=0 → S = constant

3) isotherme compression: dS=dQCD/T2 4) adiabatic compression: dS=0 → S = constant Polymer Thermodynamics 24 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

Statistical Interpretation of Entropy Number of possible configuration for 3 distinguishable particles in 3 rooms

ε3

ε2

ε1

Number of possible configurations corresponds to the permutations of the number of particles: P=N! = 3*2*1 = 6 N ! probability: W = NNN123!!!… Ni ! W is called „thermodynamic probability“ and it is the number of possible configuration for a given macroscopic state. Polymer Thermodynamics 25 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

Example: distribution of 4 particles with identical energy in 4 volumes.

A WA= 4!/(4!0!0!0!)= 4!/4! =1

B WB= 4!/(3!0!1!0!)= 4!/3! =4

C WC= 4!/(2!1!1!0!)= 4!/2! =12

D WD= 4!/(1!1!1!1!)= 4!/1! =24

The macroscopic state D can be realized by the most configurations. The macroscopic state D has the highest thermodynamic probability. Polymer Thermodynamics 26 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Statistical interpretation Ice melting – S = k lnW classic example of entropy k Boltzmann-constant increasing described -23 k=R/NAV=1.38 10 J/K in 1862 by R. Clausius as an increase in the disgregation of the molecules of the absolute values of entropy are known body of ice.

⎛⎞W2 Δ=SSSk21 − =ln ⎜⎟ ⎝⎠W1

In statistical thermodynamics the entropy is defined as a number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system. Polymer Thermodynamics 27 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

The entropy of an isolated system can never decrease, but always increases for irreversible processes or stays constant for reversible processes.

irreversible isolated systems dS ≥ 0 reversible

open and irreversible closed Δ≥Stotal 0 systems: reversible

ΔSStotal=Δ system +Δ S surrounding ≥0

A. Einstein: The second law of thermodynamics is the premier law of all sciences. Polymer Thermodynamics 28 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

Dickerson/Geis „Chemie eine lebendige und anschauliche Einführung“ Polymer Thermodynamics 29 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

irreversible N O dS ≥ 0 2 2 reversible

for isolated systems air Reason: The spontaneous demixing of air leads to a smaller number of microscopic configurations and hence to a decrease of entropy.

N2 O2 disagreement to the second law of thermodynamics Polymer Thermodynamics 30 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

n1=n2, ,,cp1=cp2 (i.e. water) T =298 K dQ =-dQ =dQ 1 T2=318 K 1 2 First law of thermodynamics gives information

of the resulting temperature T3.

Second law of thermodynamics gives information in which direction this process dQ ? takes place. dQ1 ? T3 ? 2

dStotal =+ dS12 dS

dQ12 dQ ⎛⎞11 dStotal =+= dQ ⎜⎟ − 298K 318KKK⎝⎠ 298 318 ⎛⎞318KK− 298 dStotal =→ dQ⎜ ⎟ ≥ 0 dQ ≥ 0 ⎝ 298KK *3 18 ⎠ Polymer Thermodynamics 31 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

T =298 K 1 T2=318 K

dQ ? dQ1 ? T3 ? 2

If two systems having different temperatures are in thermic contact results in the heat flow from the system with higher temperature to the system with lower temperature, never the other way around. Polymer Thermodynamics 32 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

The hot coffee in the cup will be cooled down in a cool room. The opposite procedure that means the cafe will be heated and the room will be cooled down will never happen.

Reason

Second Law of Thermodynamics Polymer Thermodynamics 33 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics

irreversible dS ≥ 0 reversible

dQrev We would produce dS = only cold water. T

alternative formulation of second law of thermodynamics

There is no perpetual motion of the second kind. This device uses the heat of a reservoir and transfer it into mechanical energy. Polymer Thermodynamics 34 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Example

A piece of steel with a mass of 40 kg and a heat capacity of cP,steel=0.5 kJ/(kg*K) should be cooled down applying an oil bath having a heat capacity of cP,oil=2.5 kJ/(kg*K). The steel has a temperature of 450°C. The amount of oil at 25°C to be available is 150kg. Is this procedure possible ?

dQsteel= − dQ oil TT m c dT=− m c dT → m c T − T =− m c T − T steel steel∫∫ oil oil steel steel() steel oil oil oil () TTsteel oil kJ kJ 40 kg *0.5 ()TKkg−=−723.15 150 *2.5 ()TK− 298.15 kg K kg K →=TK319.67 Polymer Thermodynamics 35 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics Example

T2 dQ mcPP dT mc dT⎛⎞ T2 dS== →Δ= S = mcP ln ⎜⎟ TT∫ T T T1 ⎝⎠1 kJ ⎛⎞319.67 K kJ Δ=Skgsteel 40 *0.5 ln ⎜⎟= -16.33 kg K ⎝⎠723.15 K K kJ ⎛⎞319.67 K kJ Δ=Skgoil 150 *2.5 ln ⎜⎟= 26.13 kg K ⎝⎠298.15 K K kJ kJ kJ Δ=S -16.33 + 26.13 = 9.8 > 0 total KKK Polymer Thermodynamics 36 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function - entropy

SfTPnnn= (, ,12 ,… i ) ⎛⎞∂∂∂SSS ⎛⎞ ⎛⎞ dS=++⎜⎟ dT ⎜⎟ dP⎜⎟ dn1 ⎝⎠∂∂∂TPnPnnn,,.. ⎝⎠ Tnnn ,,.. 1 12ii 12 ⎝⎠PT,, n21 .. nj≠ ⎛⎞∂∂SS⎛⎞ +++⎜⎟ dn2 … ⎜⎟ dni ∂∂nn2 i ⎝⎠PT,, n12 .. ni≠ ⎝⎠PT,, n12 , n .. nii≠

assumption: pure substance ⎛⎞∂∂SS ⎛⎞ dS=+⎜⎟ dT ⎜⎟ dP ⎝⎠∂∂TPPT ⎝⎠ Polymer Thermodynamics 37 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function - entropy

⎛⎞∂∂SS ⎛⎞ SfTP= (, )→=dS⎜⎟ dT + ⎜⎟ dP ⎝⎠∂∂TPPT ⎝⎠ ⎛⎞∂SdQ ⎜⎟==? reversible change of state dS ⎝ ∂TT⎠P

isobaric change of state of ideal gases dQ= CP dT

CdTP ⎛⎞∂SCP →=dS ⎜⎟= T ⎝ ∂T ⎠P T Polymer Thermodynamics 38 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function - entropy ⎛⎞∂∂SS ⎛⎞ SfT= (,P )→=dSdTdP⎜⎟ + ⎜⎟ ⎝⎠∂∂TPPT ⎝⎠ ⎛⎞∂SdQ ⎜⎟=→? reversible change of state dS = ⎝⎠∂PTT isothermal change of state dQ= PdV ideal gas nRT= PV dQ PdV dS == TT ⎛⎞∂VnRT nRT P nR T nR =− → dVdPdS=− =− dP=− dP ⎜ ⎟ 2 2 2 ⎝⎠∂PPT P T P P ⎛⎞∂SnRV → ⎜⎟=− =− ⎝⎠∂PPT T Polymer Thermodynamics 39 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function - entropy

⎛⎞∂∂SS ⎛⎞ S = fT(,V ) →=dS⎜⎟ dT + ⎜⎟ dV ⎝⎠∂∂TVVT ⎝⎠ ⎛⎞∂SdQ ⎜⎟==? reversible change of state dS ⎝⎠∂TTV

isochoric change of state of ideal gasesdQ = CdTV

CdTV ⎛⎞∂S CV → dS =→⎜⎟= T ⎝⎠∂T V T Polymer Thermodynamics 40 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function - entropy

⎛⎞∂∂SS ⎛⎞ SfTV= (), →=dS⎜⎟ dT + ⎜⎟ dV ⎝⎠∂∂TVVT ⎝⎠ ⎛⎞∂SdQ ⎜⎟=→? reversible change of state dS = ⎝⎠∂VTT isothermal change of state of ideal gases dQ= PdV dQ PdV ⎛⎞dS P dS == →⎜⎟= TT ⎝⎠dVT T Polymer Thermodynamics 41 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function - entropy CV dS=−P dT dP TT C P dS=+V dT dV TT

The entropy of an ideal gas increases with increasing temperature and/or volume. The entropy of an ideal gas decreases with increasing pressure. Polymer Thermodynamics 42 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function F ≡ UTS− free energy = Helmholtz energy FJ[ ] dF= dU−− TdS SdT

dU=+ dQrev dW

with dQrev ==− TdS dW PdV dU=− TdS PdV dF= TdS −−PdV TdS −=−−SdT PdV SdT dF=− PdV − SdT for dV=→0 dF =− SdT Polymer Thermodynamics 43 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function F = UTS− dF= −− PdV SdT FfVT= (,) ⎛⎞∂∂FF ⎛⎞ dF=+⎜⎟ dV ⎜⎟ dT ⎝⎠∂∂VTTV ⎝⎠ ⎛⎞∂∂FF ⎛⎞ ⎜⎟= −=−PS ⎜⎟ ⎝⎠∂∂VTTV ⎝⎠ Polymer Thermodynamics 44 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function GHTS≡ − G = free enthalpy = Gibbs-energy dG= dH−− TdS SdT GJ[] H=+ U PV → dH = dU + PdV + VdP

dU=+ dQrev dW

dQrev ==− TdS dW PdV dU=− TdS PdV dH=− TdS PdV + PdV +=+VdP TdS VdP dG= TdS +−VdP TdS − SdT dG= VdP − SdT Polymer Thermodynamics 45 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics state function

GHTS≡ − dG= VdP− SdT GfTP= (, ) ⎛⎞∂∂GG ⎛⎞ ⎛⎞∂∂GG ⎛⎞ dG=+ dT dP ⎜⎟=−SV ⎜⎟ = ⎜⎟ ⎜⎟ ∂∂TP ⎝⎠∂∂TPPT ⎝⎠ ⎝⎠PT ⎝⎠ for isobaric process (dP=0) dG= − SdT Polymer Thermodynamics 46 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics equilibrium conditions state function dT== dV 0 dT= dP = 0

⎧< 0⎫⎧ voluntary ⎫ ⎧⎫⎧< 0 voluntary ⎫ ⎪ ⎪⎪ ⎪ ⎪⎪⎪ ⎪ dF ⎨= 0⎬⎨ equilibrium ⎬ dG ⎨⎬⎨= 0 equilibrium ⎬ ⎪ ⎪⎪ ⎪ ⎪⎪⎪ ⎪ ⎩⎭⎩> 0constraint ⎭ ⎩⎭⎩> 0 constraint ⎭

at equilibrium dF=0 at equilibrium dG=0 minimum of free energy minimum of free enthalpy

general equilibrium conditions Polymer Thermodynamics 47 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics equilibrium conditions state function

EPot = mgh

stable instable metastable

EPot→ global minimum EPot→ global maximum EPot→ local minimum stable against all instable against all stable against small perturbations perturbations perturbations Polymer Thermodynamics 48 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics equilibrium conditions state function

dS=0 equilibrium Entropy S

state variable Polymer Thermodynamics 49 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics equilibrium conditions state function

equilibrium

dG=0 free enthalpy G state variable Polymer Thermodynamics 50 2. First and Second Law of Thermodynamics 2.1. Second Law of Thermodynamics equilibrium conditions state function

equilibrium

dF=0 free energy F

state variable