物理化学双语chap2a

2 T1 T2
H na dT nb TdT nc dT / T
T1 T1 T1 1 2 2 2 2 1
T2
T2
T22ຫໍສະໝຸດ 1 1 H naT nb(T T ) nc T2 T1
Hess’s Law
products C
HA-C = HA-B + HB-C
w pex dV
V1 V2
if reversible , pex p gas if an ideal gas, p gas nRT / V dV V2 w nRT nRT ln V V1 V1
V2
Isothermal Irreversible Work
w pex dV
V1
V2
if irreversib le, pex const . w pex dV pex V
V1 V2
Adiabatic Expansion
• dq=0 • dU=dw • for an ideal gas, CVdT = -pexdV • if reversible, pex = p = nRT/V • therefore, CV(dT/T) = -nR(dV/V)
w
q
q
Reversible Adiabatic Expansion
CV dT pex dV pdV nRT CV dT dV V dT dV CV ,m R T V Tf Vf CV ,m ln R ln Ti Vi
Reversible Adiabatic Expansion
1 meter
1 kg
State Function vs. Path Function
• A state function is a property of a system that depends only on its current state and not on how that state was reached. • A path function depends on how the state was reached.
r C p dT
n J C p ,m ( J )
J
0 Hf
Examples
• Acetic Acid 2C(gr) + O2(g) + 2H2(g) CH3COOH(l) • Ammonium Nitrate N2(g) + 2H2(g) + 3/2 O2(g) H4O3s) • Sodium Chloride Na(s) + 1/2 Cl2(g) NaCl(s)
A
• The enthalpy change for an overall reaction is the sum of the enthalpy changes of the individual reactions into which a reaction may be divided.
BC
The First Law
The Concepts
System and Surroundings
• System - the part of the world in which we have a special interest.
• Surroundings - where we make our observations.
Energy
• Isolated - no interchange with surroundings.
Heat
• Heat is the energy transferred between a hot object and a cold object.
• Temperature is the degree of “hotness” of an object.
pex pgas
Irreversible Changes
• An irreversible change is one that is not reversible. • In an irreversible expansion, pex < pgas
• In an irreversible compression, pex > pgas
CO2(g) H2O(l) C (gr) a b/ 44.22 75.29 16.86
10 K
-3 -1
c/
10 K
5
2
8.79 0 4.77
-8.62 0 -8.54
Cp,m = a + bT + c/T2 in J/mole
Variation of H with Temperature
d H nC p dT H n (a bT c / T )dT
• Given Hf0 values for all the reactants and products, H0 may be calculated for any reaction.
Temperature Dependence of rH
rH(T2)
Reactants(T2)
HR Reactants(T1) rH(T1)
U CV dT pex dV assume p ex constant CV T f Ti pex V f Vi
Argon: Adiabats vs. Isotherms
2
p / atm
1
adiabat isotherm
0 0 20 40 60 80
V/L
Hess’ Law and
0 Hf
• For the reaction 2A + B 3C + D,
• For the general reaction SnJJ = 0, H0SnJHf0(J)
H0 3Hf0(C) + Hf0(D) - 2Hf0(A) - Hf0(B)
system
surroundings
Types of Systems
• Open - exchanges matter and energy with surroundings. • Closed - exchanges only energy with surroundings.
Matter
Energy
T1 T2
U
T
slope = CV
Heat Capacity: Cp,m
H Cp T p d H dq p n C p ,m d T H q p n C p ,m d T
T1 T2
H
T
slope = Cp
Temperature Dependence of Cp,m
dz
gas
dw = - pex dV
A
Reversible Changes
• A reversible change is one that can be reversed by an infinitesimal modification of a variable.
• In a reversible expansion or compression, pex = pgas
Tlow q
Thigh
Isothermal vs. Adiabatic
• An adiabatic process in one in which no heat is exchanged between the system and its surroundings. • An isothermal process in one in which the initial and final temperatures are the same. • Isothermal processes are not necessarily adiabatic.
CV ,m ln Tf T i Tf Ti
CV ,m R
R ln
Vf Vi
Vi V f c c T f V f Ti Vi
where c C V, m / R
Reversible Adiabatic Expansion
T f V f Ti Vi
Enthalpy and Heat
• Enthalpy is defined H = U + pV
• dH = dU + pdV + Vdp • at constant p, dH = dU + pdV dH = dqp
Heat Capacity: Cv,m
U CV T V d U dqV n CV ,m d T U V qV n Cv ,m d T
pex pgas
pex
pgas
Indicator Diagram: compression
10
T = 273 K
8 6
additional irreversible work
pex
4 2 0 0
reversible work
Vf5
10
Vi 15
20
Isothermal Reversible Work
Products(T2) HP
Products(T1)
rH(T2) = HR + rH(T1) + HP
Kirchhoff’s Law
H R
T2 T1
C ( R ) dT p , m
T2 T1
r H ( T2 ) r H ( T1 ) w here r C p