First law for closed systems

1
Lecture 3
?

• First law for closed systems
• Volume work
• Meaning of volume integral
• Reversible versus irreversible expansion
• Reversible expansion ideal gas

2
Ideal Gas Law does not discriminate molecules
?
?
State Pressure P Volume V
Moles n Temperature T
velocity v
?
Equation of state
PV nRT
for ideal gas
mass m
3
Energy is conserved ?U 0 for isolated systems
?
isolated system
Bromine (liquid) Phosphorus (solid)
4
First Law closed system ?U q w
?
w lt 0
w gt 0
work w
Zn 2H Zn2 H2
heat q
q gt 0
q lt 0
5
?U U2 U1 q w
?
?
?
?U independent of path (state variable)
Zn2
2
Zn
1
?
q w are path dependent
w -p?V wextra
6
Work performed by expanding gas
?
h
?
Work force x distance w -?mgdz dw
- Fdz -mg ?dz - mgdz -
mgh (lt0)
0
h
0
?
The gas has lifted a weight mg over a distance h
against gravity
7
Work expanding gas w ?PdV
?
Pex
F A
surface area A Pex
Zn 2H Zn2 H2
?
work against external P
small change in volume V
work force x distance
8
Graphical meaning of w - ?PexdV
?
Pex
V2
Pex
V1
Pex changes
(?)
V1
V2
volume V
?
In general Pex not known a priori
9
Constant external pressure Pex
?
V2
Pex 1 atm
V1
lt0
gt0
?
Same expansion against vacuum w ?
10
Work w can be calculated for a reversible process
?
H2
?H H1 - H2
RACE
H1
Limit infinitely slow path reversible path
11
Reversible versus irreversible (spontaneous)
expansion
?
Pex
P1Pex
Reversible expansion is sequence of equilibrium
states
12
Reversible expansion of ideal gas
?
isothermal T constant PV nRT (ideal gas)
lt 0
13
Reversible vs. irreversible paths
?
Pex
irreversible expansion path
Pex
P
V1
P
reversible path
?
w ? state variable wrev ? wirrev
14
Lecture 4
?

• Reaction heat
• Enthalpy
• Exo- and endothermic reactions
• Hess law
• Standard state and standard enthalpy
• Heat capacities

15
Application First Law Enthalpy H
?
q
1 mole hexane ethanol etc.
How much heat is produced by a reaction?
?
volume work w
Chemistry at constant pressure
q
Pex 1 atm
reaction
?
Energy U is a state variable
16
Decomposition of H2O via two different paths
?
electrolysis
H2O H2 ½ O2 State 1 State 2 P1 V1
U1 P2 V2 U2
high T
?
Enthalpy change
?H ?U P?V P constant qP w P?V
First Law qP we P?V P?V qP we
qP only volume work we 0
?
At P constant, qP is a state variable
17
Enthalpy H reaction heat at constant P
?
lt 0 exothermic
?H qP
gt 0 endothermic
?
State variable!
breakfast
sugar CO2 H2O ?H
burn with Bunsen burner
18
Do-it-your-self slides
Study the following slides on enthalpy and its
applications
19
Hess Law
?
A
1
3
C
B
2
A B ?H1 B C ?H2 A C ?H3 ?H1 ?H2

20
Application
?
urea
glycine
3) 3O2 2 NH2CH2COOH H2NCONH2 3 CO2 3
H2O ?H3 ? 2) 3O2 2 glycine 2NH3 4
CO2 2 H2O ?H2 -1163.5 kJ/mol 1) H2O
urea 2 NH3 CO2 ?H1 133.3 kJ/mol
3
2
1
?
?H3 -?H1 ?H2 -1296.8 kJ/mol
21
2 H2 O2 2 H2O ?H
?
?
?H H - H - H ?Hf0
1 2
H2O
O2
van H2O
H2
enthalpy H2O
Enthalpy
enthalpy O2
enthalpy H2
?
What is the reference state?
22
Definition standard enthalpy
?
23
Example combustion of ethanol
?
C2H5OH(l) 3 O2(g) 2 CO2(g) 3
H2O(g)
?
-393.51
-276.98
H0 (kJ/mole)
-241.82
CO2
EtOH
H2O
elements C, H2, O2
24
Calculate reaction enthalpy from standard
values
?
?H0 2 H0(CO2, g) 3H0(H2O, g) - H0(O2, g)
H0(C2H5OH, l) - 1235.4 kJ mole-1
0
25
Heat capacity C dq / dT
?
T1
T2 gt T1
?


D
w
q
U
C?T C(T2-T1)
T
2
?
ò

dT
C
q
T
1
?
ò
ò


dT
C
q
dT
C
q

V
V
P
P
constant V
constant P
26
Summary enthalpy H
?
Pex 1 atm
H2 gas
Zn 2H Zn2 H2
1
2
qP
?
?U q w q -? PdV no other work we
0 qp - ? PdV P constant
27
Enthalpy H U PV
?
?H ?U P?V P constant qP
?
Enthalpy change reaction heat at constant P
?
qP lt 0 exothermic gt 0 endothermic
28
First Law Energy is conserved
?
?

• Isolated system ?U 0

two types of (ir)reversible energy exchange with
surroundings
two types of work
A
?H1
?H2
H U PV, we 0, constant P
B
C
?H qP
?H3