chapter 2 the first law 2.1 the basic concepts thermodynamics field of physics that describes and...
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Chapter 2 The First LawChapter 2 The First Law
2.1 The basic concepts
Thermodynamics field of physics that describes and correlates the physical properties of macroscopic systems of matter and energy.
1.1.1 System and surrounding
System the parts of the world in which we have a special interest.
Surroundingswhere we make our measurement.
system water Open system
system water+ vapor
Closed system
system water+gas
Isolated system
adiabatic
2.1.2 Thermodynamic properties
Pressure p , volume temperature V , temperature T ,
internal energy U, enthalpy H , entropy S ……
extensive property extensive property = intensive property
m
VV
n
m
V e.g.
e.g mass, volume
Extensive property a property that depends on the amount of substance in the sample.
e.g. Temperature , pressure , density
Intensive property a property that is independent of the amount of substance in the sample.
2.1.3 Definition of phase
Phase a homogeneous part of a system.
Homogeneous system one phaseHeterogeneous system two or more phase, interface
2.1.4 The equilibrium state
Thermal equilibrium T1= T2 = T3=… = Tex
Mechanical equilibrium p1= p2 = p3=… = pex
Phase equilibrium = = =…
Chemical equilibrium A= B= Y = Z …
Thermodynamic state—— equilibrium state:
2.1.5 State and state function
The value of a state function depends only on the present state of the system and not on its past history.
The state of a macroscopic system in equilibrium can be described in terms of such measurable properties as T, p, and V, which are known as thermodynamic variables( or state functions).
State description Classical mechanics:Thermodynamics: p,V,T…
,r p
2.1.6 Process and path
Process When a macroscopic system moves from one state of equilibrium to another, a thermodynamic process is said to take place.
Path
(b)Isobaric process p1 = p2 = pex
(a)Isothermal process T1 = T2 = Tex
(c)Isochoric process V1 = V2
(d)Adiabatic process Q=0
(e)Cyclic process
1. p, V, T process
(f)expansion against constant pressure pex=constant
(g) free expansion pressure pex=0
2 . Phase transition process
aA + bB = yY + zZ
0 = ΣBB
nB,0 is the number of mole of substance B present at the start of the reaction .
3 . Chemical reaction process
B —stoichiometric number of B
nB = nB,0 nB =B , d nB = B d
A= - a , B= - b , Y= y, Z= z
extent of reaction — , units is mol 。1 1
B B B Bd d Δ Δn n or
2.1.7 Work and heat
W>0 W is done on the system by the surroundings
W <0 system does work on its surrounding
Work The energy transfer between system and surroundings due
to a macroscopic force acting through a distance
Heat The energy transfer between system and surroundings due to a temperature difference
Q>0 when heat flows into the system from the surroundings
Q<0 when heat flows into the surroundings from system
2.1.8 Internal energy U
Type of workType of work ddWW
ExpansionExpansion
Surface expansionSurface expansion
ElectricalElectrical
--ppexexddVV
ddAA
ddqq
(2) U is an extensive property;
(1) U is state function ;
(3) the absolute value of U is unknown.
The total energy of system
2.2 The first law
U =U2 - U1 = Q + W closed
system dU = δQ + δW U= Q+W
Isolated system
Cyclic process
Adiabatic process
Q=0, W=0 , U=0
U=0, Q= W
Q =0, U = W
Conservation of energy
It is impossible to built a first kind of perpetual motion machine.Work and heat dU = Q + W
2.2.1 Expansion work
ex ex exδ dz d dW F p A z p V
2
1exd
V
VW p V
1. Free expansion
pex=0, W=0
2
1su su 2 1
ex
d ( )V
VW p V p V V
p V
-
2.Expansion against constant pressure
3. Reversible expansion
Different expansion
Reversible expansion
W= - pexdV = - pdV
2
1r d
V
VW p V
Quasi-static process
Isothermal reversible expansion
Consider the isothermal, reversible expansion of a perfect gas:
2
1
2
1
2
1
2
1
d
d
d
ln
V
V
V
V
V
V
W p V
nRTV
VT
nR VVV
nRTV
Reversible process
One where the system is always infinitesimally close to equilibrium and an infinitesimal change in conditions can reverse the process to restore both system and surroundings to their initial state.
Characteristic
(a) Infinitesimally close to equilibrium.
(b) Tex = T ; pex = p.
(c) Both system and surroundings can be restore to their
initial state through reverse process.
2.2.2 Heat transaction
Consider closed system
dU = Q + W = Q + Wexp + W’
dV=0, W’=0 , dU = QV , U = QV
(a) Calorimetry
A constant-volume bomb calorimeter. The `bomb' is the central vessel, which is massive enough to withstand high pressures. The calorimeter is the entire assembly shown here. To ensure adiabaticity, the calorimeter is immersed in a water bath with a temperature continuously readjusted to that of the calorimeter at each stage of the combustion.
Definition of molar heat capacity
m
def 1( )
d
QC T
n T
(b) Heat capacity
Molar heat capacity at constant volume
,m
def ( ) δ1 1( )
dV V
VV
C T Q UC T
n n T n T
2
1
,m ( )d
T
V VTQ U nC T T
(c) Enthalpy
def H U pV
W =- pexV
W =- pexV, W′ = 0 , U = Qp - pexV
U2 - U1 = Qp - pex(V2 - V1)
p1 = p2 = pex
U2 - U1 = Qp - (p2 V2 - p1V1)
Qp = (U2 + p2 V2) - (U1 + p1V1) = (U + pV)
Isobaric process
(1) H is state function ;
(2) H is an extensive property;
(3) the absolute value of U is unknown.
Enthalpy
For a closed system,
p=const . W’=0
Qp = H
δQp = dH
Cp , m = a + bT + cT 2 + dT 3
or Cp , m = a + bT + c′T - 2
approximate empirical expression
2
1
,m ( )d
T
pTH nC T T
,m
( ) δ def 1 1( )
dp p
pp
C T Q HC T
n n T n T
Molar heat capacity at constant pressure
Perfect gas Cp,m-CV,m=R
2424
2.2.3 Adiabatic changes
dU = CVdT, dU = W
2 2
1 1
,m d d
T T
V VT TW U C T nC T if CV,m=const.
W = U = n CV,m(T2 - T1)
(a) The work of adiabatic change
dU = δW,
if δW′ = 0 then CVdT =- pexdV
Reversible process, pex = p,
perfect gas ddV
VC T nRT
V
d d0
V
T nR V
T C V
perfect gas Cp - CV = nRd d
0p V
V
C CT V
T C V
perfect gas γ=constant
(b) heat capacity ratioγ and adiabatsd d
( 1) 0T V
T V
def /p VC C
ln{ T } + (γ1) ln{ V } = constant TVγ-1 = constant
pVT
nR constantγpV
nRTV
p (1 ) / constantTp
( perfect gas, reversible process, closed system, W′ = 0 .)
Equations of adiabatic reversible process
2
1
d
V
VW p V
pV =constant
1
1 1 1
2
11
p V VW
V
1
1 1 2
1
11
p V pW
p
(c) Work of adiabatic reversible process of perfect gas
2.2.4 Phase transition
1. Enthalpies of phase transition
T=const. , p =const. ,W'=0 pQ H
vaporization :vapH m,
fusion : fusH m,
sublimation : subH m,
transition: trsH m
Enthalpy of
2. Expansion work of phase transition
at constant T and p
W =- p(V - V)
β-gas phase,α-liquid phase (or solid phase)
V >>V, W - pVβ
β perfect gas W =- pVβ =- nRT
3. U of phase transition
U = H - p(Vβ - Vα)
Vβ>>Vα, U = H - pVβ
perfect gas U = H - nRT
U = Qp + W
2.3.1 Molar enthalpies and internal energies of chemical change
BB
0 BaA + bB = yY + zZ
Br m
B
U UU
n
B
r mB
H HH
n
2.3 Thermochemistry
2.3.2 Standard enthalpy changes
mr m B
def ( ) (B, )H T H T ,yy
Standard molar enthalpies of the substance B at temperature T
and pressure p 。
(B=A, B, Y, Z; =phase state)
2.3.3 Standard states of substances
Standard pressure p= 100kPa
gas: p = p , T, perfect gas
solid or liquid : pex = p , T
rHm (T) = yHm
(Y, , T ) + z Hm (Z, , T )
- a Hm (A, , T ) - b Hm
(B, , T )
For reaction aA + b B →yY + zZ
Pure, unmixed reactant in their standard states Pure, separated products in their standard states
2.3.4 Relation between rHm and rUm
For a reaction B
BB0
rH m (T, liquid or solid) ≈rU m
(T, l or s)
rHm ( T) = rUm (T) + RT B (g)
rH m (T) = BH m
(B, , T )
= BU m (B, ,T ) + B[p V m (B,T)]
T= Constant V=constant W′ = 0 QV = rU
T= Constant p=constant W′ = 0 Qp = rH
2.3.5 Hess’s law
A Cr mΔ ( )H Ty
Br m,1Δ ( )H Ty
r m,2Δ ( )H Ty
rHm (T ) = rHm,1 (T ) + rHm,2 (T )
The standard enthalpy of overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided.
rHm (T) in term of fHm
(B, ,T )
r Hm (T) = Bf Hm
(B, ,T )
reactants
elements
products
r Hm
Ent
halp
y,
H
2.3.6 Standard enthalpies of formation fHm (B, ,T )
r m B m
def ( ) (B,phase state ) H T H T ,yy
rHm (T)in term of cHm
(B, ,T )
r Hm (T) = – BcHm
(B, ,T ) *r m B m
def ( ) (B,phase state ) H T H T ,yy
reactants
CO2(g), H2O(l)
products
r Hm
Ent
halp
y, H
2.3.7 Standard molar enthalpies of combustion cHm
(B,phase state ,T )
2.3.8 The temperature dependence of reaction enthalpies
1H y2ΔH y
4ΔH y3ΔH y
r m 1Δ ( )H Ty
aA + bB yY + zZ
r m 2Δ ( )H Ty
aA + bB yY + zZ
r H m (T1) = H 1 + H 2 + r H m (T2) + H 3 + H 4
2
1
Br m 2 r m 1 ,m Δ ( ) Δ ( ) (B)d
T
pTH T H T C T y y
2
1
1 ,m Δ (A)d ,
T
pTH a C T y 2
1
2 ,m Δ (B)d ,
T
pTH b C T y
2 2
1 1
3 ,m 4 ,m Δ (Y)d , Δ (Z)d
T T
p pT TH y C T H z C T y y
B Cp,m(B)=yCp,m(Y) + zCp,m(Z) - aCp,m(A)- bCp,m(B)
If T2 = T,T1 = 298.15K,
Kirchhoff’s law
2
Br m r m ,m 298.15KΔ ( ) Δ (298.15K) (B, )d
T
pH T H C T y y
2
1
Br m 2 r m 1 ,m Δ ( ) Δ ( ) (B)d
T
pTH T H T C T y y
2.4 State function and exact differentials
2.4.1. Exact differentials
d d dy x
Z Zz x y
x y
Z = f (x, y ),
2.4.2 Internal energy
d d d
d d
T V
VT
U UU V T
V T
UV C T
V
U = f (T, V ),
The Joule experimentT
U
V
=0
Perfect gas dU=CVdT, or U=f(T)
2
1
Δ dT
VTU C T
2.4.3 Enthalpy
d d d d dppT T
H H HH p T p C T
p T p
H = f (T, p ),
dH=CpdT, or H=f(T) 2
1
Δ dT
VTU C T
Perfect gasT
H
p
=0
2.4.4 The Joule-Thomson effect
Q = 0
U = W
or U2 - U1 = p1V1 -
p2V2 U2 + p2 V2 = U1 + p1
V1 H2 = H1
W = p1V1 - p2V2
Isenthalpic process U= f(T)
Joule-Thomson coefficient
J-T
def
H
T
p
p < 0,
J-T < 0, heating ;
J-T > 0, cooling ;
J-T = 0, T unchanged