Sect. 1 Basics of Thermodynamics1

7/30/2019 Sect. 1 Basics of Thermodynamics1

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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 andimaginary boundary sections through which fluid passes

2

surroundingssurroundings


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Example of a more complex system:

gas-cylinder blowdown


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Boundary

the boundaryencloses 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

1. single component:pure substance

2. two componentsbinarysystem

a pure substance can become a binary system:

steam is a single component; but at very high T, itdissociates 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 singlecomponent 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 anonreacting 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 O2is a nonreacting ternary; at high temperature, it is

a reactive ternary (H, C, and O) with manychemical 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 vaporif it iscondensible (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 phasesseparated 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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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, ,


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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 ina 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 andclassical thermodynamics (F is rarely

used in purely classical approach)

Gibbs free energy: G H TS- G is the criterion of equilibrium in chemical

reactions

- G 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 azero value at an arbitrary reference state (thesame state for all four)


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Extensive and Intensive properties

Extensive: value proportional to amount insystem: V, U, S, H, F, G

Intensive: value independent of the amount ofmaterial: 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 reciprocalof 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:

= (1/v)(v/T)P - thermal expansion

(Hg) used for mercury thermometer = -(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 atmtemperature: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 = mv2 kg-m2/s2; but from F = ma, N = kg-m/s2

kg-m2/s2= N-m = J


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Thermodynamic Stateof 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 T

Mechanisms (not thermodynamic)

- conduction: molecular motion- convection: bulk fluid movement

- radiation : electromagnetic fields

Heat is not a thermodynamic property: itcauses changes in them


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Work: (W)

Expansion (pV ): W = Fx = (F/A)(Ax) = pV Shaft: rotation of a shaft by a moving fluid

Electrical: flow of electrons down a potentialgradient

External: all Fx except pV;

why? pV is often not useful work: just pushingback or being pushed by the surroundingatmosphere

Work is not a thermodynamic property, but canchange them

All forms of work are theoretically interconvertible


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Thermodynamic Processes

-Process - change in p-V-T

state of system due toexchange of heat and/orwork 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 Cannot infer Q from thisdiagram

Path depends on how Tvaries with V.=

2

1

V

V

dV)V(pW


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ISO processes In most processes, one property is constant:

Process

Restraint

Property

constant Example

isothermal T Melting ice

isobaric p Heat gas in

cylinder/piston

isochoric V Heat gas in

closed vessel

isentropic S Gas cylinder

blowdown

cyclic - Returns to

Initial state


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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 donereversibly is always > 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 bythe surroundings

( foV

V

V

VrevV/VlnnRTV/dVnRTpdVW f

0

f

0

===


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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

( 55.013

3ln

1V/V

V/Vln

W

W

fo

fo

irr

rev

===

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 reversiblethan 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 p, T orm)


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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 entropyis a maximum (mainly oftheoretical 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 WelU = 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 thesystem and the surroundings:

Usys= (Q W)sys

Usurr= -(Q W)surr

Add the 1st Laws for system & surroundings:

Usys+ Usurr= 0

This is the Law ofConservation of Energy


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Where the 1st Law is inadequate Consider an isolated system consisting of two

rigid subsystems of different temperatures thatcommunicate 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 thetwo 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 2ndLaw was discovered by Clausius from

numerous observations showing that ifa process isreversible, 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 thesymbol S:

21

rev

T

Qd

= 21

rev12

T

QdSS


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Irreversible processes

Forirreversible processes, the equality no

longer holds. Instead:

In irreversible processes, entropy is created!

Other forms of the 2nd Law:

dS

21

12T

QdSS

==2

1

revrev 0

T

QandTdSQ;

T

Q


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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 (Tsurr>Tsys)

entropy can be produced but never destroyed

2

1sys

sys T

Q

S

2

1surrsurr T

Q

S

0SS surrsys


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The direction of heat flow revisited begin with: S1 + S2 > 0

but S1 = Q1/T1 and S2 = Q2/T2 (heat flow to and fromreservoirs is reversible)

T1 T2, is the source of irreversiblity

Q1/T1 + Q2/T2 > 0; from 1st Law: Q1 = -Q2

If T1>T2, then Q2 >0

and Q1


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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 (U = 0):

Irreversible version:

initial state (To) final state(T

o)

Boltzmann eqn: S=nNAvklnW; S=nRln(Wf/Wo) = nRln2


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Reversible version:


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U = 0 for the reversible process as well

from the 1st Law, Q = W

work can be calculated for the reversibleprocess only

From the 2nd Law:S = 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 thesame as the S for the irreversible process

(but, work was done in reversible process)

( QV/VlnnRTpdVW 0fVV

f

0

=

E t F E d E ilib i


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Entropy, Free Energy and Equilibrium

du = Tds pdv - wext

isolated system, dv = du = 0

Equilibrium: system cannot perform external work, or dwext = 0

- Electrical (battery)

- Chemical (ATPmuscle)

For reversible process: Tds pdv

for a closed system: du = q - w(PV) -wext

dsu,v = 0 sState of

system

equilibrium state

At equilibrium with u & v constant

the entropy is a maximum

= small increment of heat or work

d = small increment of a thermodynamic property

Th l ilib ti f id ti l lid


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Thermal equilibration of identical solids

T1

Q

T2Tf Tf

energy conservation:

UTot=U1+U2= 0

CV(Tf T1) + CV(Tf T2) = 0 Tf= (T1 + T2)

STot = S1 + S2 =

=

21

2

fV2

fV1

fVTT

TlnC

T

TlnC

T

TlnC

Eliminate Tf:

=

21

2

21VtotTT4

)TT(lnCS

T2/T1 STot/CV

0.9 0.0028

1.0 01.1 0.0023

Thermal equilibration results in an increase in

the entropy of the isolated system

Enthalp


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h u + pv dh = du + pdv + vdp use du equation:

dh = Tds + vdp - Wext

Enthalpy

Helmholz free energy

fu 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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du = Tds pdv

dh = Tds + vdp

df = - pdv sdT

dg = vdp sdT

These were derived assumingreversible q and W(pv)

However, since they involve

only state functions (properties),

they are valid for any process

Neglecting external work:

Collectively, they are called:

1.Fundamental differentials, or

2.Tds equations (first two), or

3.Gibbs equations

Equilibrium at constant T and p


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Equilibrium at constant T and p

with dT = dp = 0:

dwext= -dg

Reversible non-pv work at constant p and T

System is at equilibrium when dwext = 0

dgT,p

= 0

At equilibrium with p & T constant

the Gibbs free energy is a minimum

dg = vdp sdT - Wext

equilibriumstate

State of

system

g

Th Ph R l


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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 calleddegrees 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 pointwhere 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 coexist2Op

f =C + 2P - Nrxn


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Sect. 1 Basics of Thermodynamics1

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