Chapter 3 (1
st
law of thermodynamics)
Lecture 10
Find work done by the gas in this cycle.
P
2P
1V
1V
2Note: work is equal to
the area:
2
1
2
1
+ for clockwise d
-irectio
for anticlockwise
n
Configuration work and processes
Often, something is held constant. Examples:
dV
= 0
isochoric or isovolumic process
dQ
= 0
adiabatic process
dP
= 0
isobaric process
dT
= 0
isothermal process
Work done by a gas
f
i
V
V
W
PdV
For isochoric process
dV
= 0, so
W =
0
For isobaric process
dP
= 0, so
W = P(V
f
-V
i
)
Work done by an ideal gas
For isothermal process
dT
= 0, so
T =
constant
.
P
nRT
V
ln
ln
f i f iV
V
V
V
f
i
dV
W
nRT
V
W
nRT
V
V
W
nRT
V
f i V VPdV
W
isothermal
C
5Free Expansion of a Gas
W=0
There is no
Example:
3 3
4000 Pa 0.3m
0.2
400
f i
W
P V
P V
V
W
m
J
Calculate work done by expanding gas of 1 mole if initial
pressure is 4000 Pa, initial volume is 0.2 m
3
, and initial
temperature is 96.2 K. Assume a two processes:
isobaric
expansion to 0.3 m
3
, T
f
=144.3 K
isothermal
expansion to 0.3 m
3
.
5
.
1
2
.
0
3
.
0
3
3
m
m
V
V
nR
V
P
nR
V
P
T
T
i
f
i
i
f
f
i
f
V
P
i fV
i
V
f
P
isothermal
expansion to 0.3 m
3
.
ln
ln
3
8.31 96.2 ln
324
2
f i f iV
V
V
V
f
i
dV
W
nRT
V
W
nRT
V
V
W
nRT
V
W
i
f
P
V
P
i
P
f
V
i
V
f
It depends on the path!
When heat enters a system, what happens
to the system’s
internal energy?
When work is done on a system, what
happens to the system’s
internal energy?
The first law of thermodynamics
U is a state function , so one can take the system
from an initial state to final state (state I to state F
by two methods :
a) By an adiabatic process (Q=0)
b) By non adiabatic pr0cess (Q
≠0)
)
)
ad
In a
U
W
In b
U
Q W
The first law of thermodynamics
Two ways to exchange energy between
a closed
system
and its surroundings (reservoir):
heat and work
Such exchanges only modify the internal energy of
the system
The first law of thermodynamics: conservation of energy
Heat
Work
reservoir
W
Q
U
Q > 0: energy enters the system
Q < 0: energy leaves the system
W > 0: work done
by
the system is positive;
energy leaves the system
W < 0: work done
by
the system is negative;
work done
on
the system
energy enters the system
• For infinitesimal processes:
pdV
dQ
dW
dQ
Adiabatic processes
W
U
Q
0
Insulating
wall
Expansion:
U
decreases
Compression:
U
increases
Isolated systems:
f
i
U
U
U
W
Q
0
0
The internal energy
of an isolated systems
remains constant
Several examples
initial state = final state
Cyclic processes
P
i, f
V
W
Q
U
0
Energy exchange between
“heat” and “work”
Idea gas-isochoric process
Isochoric process: V = constant
0
21
V
V
PdV
W
T
C
T
T
C
Q
V V
(
2 1)
(C
V:heat capacity
at constant volume)
T
C
Q
U
W
Q
U
V
P
v
T
1
T
2
Heat
reservoir
During an isochoric process, heat enters
Idea gas-isobaric process
Isobaric process: P = constant
V
P
V
V
P
PdV
W
VV
2(
2 1)
1
T
C
T
T
C
Q
p p
(
2 1)
(C
P:heat capacity
at constant pressure)
V
P
T
C
W
Q
U
P
During an isobaric expansion process,
heat enters the system. Part of the heat is
used by the system to do work on the
environment; the rest of the heat is used
to increase the internal energy.
Heat
Work
reservoir
P
v
T
1
T
2
v
1
v
2
Idea gas-isothermal process
Isothermal process: T = constant
PV
nRT
2 2 1 1 2 1 2 1
ln
V V V V V VnRT
W
PdV
dV
V
dV
nRT
V
V
nRT
V
0
2
f
U
nRT
U
2
ln
V
Q
W
nRT
During an isothermal expansion process,
heat enters the system and all of the heat
is used by the system to do work on the
environment.
During an isothermal compression process,
energy enters the system by the work done
on the system, but all of the energy leaves
the system at the same time as the heat
P
v
T
dU
dQ
dW
Ideal gas-adiabatic process
Adiabatic process:
Q
= 0
2
2
2
2
f
f
U
nRT
dU
nRdT
dU
dQ dW
PdV
f
PdV
nRdT
nRdT
PdV
f
(
)
(
)
nRT
PV
d nRT
d PV
nRdT
PdV
V dP
2
PdV
VdP
PdV
P
v
T
i
T
f
( , )
P
P V T
0
)
2
1
(
2
PdV
f
VdP
PdV
f
VdP
PdV
1 11
1
0
ln
ln
0
P
V
P
V
dP
dV
P
V
P
V
P
V
Idea gas adiabatic process
P
v
T
1
T
v
1
v
2
1
dP
dV
0
Let
f
P
V
1 1
1 1
constant
ln
PV
0
V
PV
PV
P
2
2
1
1
V
P
V
P
1
2
2
1
V
V
P
P
2 1 1 1 1 2T
T
V
V
Idea gas-adiabatic process
1
1
1
1
2
2
T V
T
V
constant
PV
P
v
T
1
T
2
v
1
v
2
1
1
1
2
2
2
P V
T
P V
T
2 1 2 11
1
V
V
V
V
V
dV
V
P
PdV
W
1
1
1 1
2
1
1
(1
)
W
PV
V
V
Work done by an idea gas in an adiabatic process
1 1
constant
PV
PV
constant
PV
P
v
T
1
T
2
v
1
v
2
2
1
(1
)
nR
W
T
T
2
2
1 1
1
(1
)
W
PV
PV
Idea gas adiabatic process
During an adiabatic
compression
process, the
environment does work on the system and increases the
internal energy.
P
v
T
1
T
2
v
1
v
2
During an adiabatic
expansion
Summary
Internal energy, heat, and work:
internal energy is the energy of the system.It is a state function.
heat and work are two ways to exchange energy between the system and the environment.
They are not state functions and depend on the path.
The first law of thermodynamics connects the internal energy with heat and
work:
U
Q W
Quasi-static
process
Character
U
Q
W
adiabatic
Q
0
U
W
isothermal
T = constant
U
0
isovolumetric
isobaric
V = constant
P = constant
U
Q
Q
C
V
T
W
0
V
P
W
W
Q
U
Q
C
P
T
2 1
ln
V
W
nRT
V
Q
W
0
Q
2 1
(1
)
nR
W
T
T
23
Latent Heat (enthalpy)
12
2
1
2
1
During Phase change, lets say from solid to liquid phase
at constant T and P, l
q
u w
u
u
P v
(
v
)
12
2
2
1
1
12
2
1
(
) (
)
Where h ca
l
u
pv
u
pv
l
h
h
lled the enthalp
y
23
3
2
From liquid to gas
l
h
h
13
3
1
From solid to gas
l
h
h
Enthalpy (history of the name)
Over the
history of thermodynamics
, several terms have been used to denote
what is now known as the
enthalpy
of a system.
Originally, it was thought that the word "enthalpy" was created by
Benoit
Paul Émile Clapeyron
and
Rudolf Clausius
through the publishing of the
Clausius-Clapeyron relation
in
The Mollier Steam Tables and Diagrams
in 1827.
Gibbs
introduced a "heat function for constant pressure" in 1875, although
the word
enthalpy
does not appear in any of Gibbs' work.
In 1909,
Keith Landler
discussed Gibbs's work on this "heat function" and
noted that
Heike Kamerlingh Onnes
had coined the modern name from the
Greek
word "enthalpos" (
ενθαλ
π
ος
) meaning "to put heat into.
H
U
PV
Difference between
H
and
U
: the additional term
pV
If
pV
is an additional
energy
associated with the system (say, a gas), and is not in
the
internal energy
U
, then where is it?
The energy
pV
is in the surroundings (typically, the atmosphere). When a
system (e.g.,
n
moles
of a gas of
volume
V
at
pressure
P
and
temperature
T
) is
created
(brought to its present state from
absolute zero
), energy must be
supplied equal to its internal energy
U plus pV
, where
pV
is the
work
done in
pushing against the (atmospheric) pressure.
This additional energy is therefore stored in the surroundings (atmosphere)
In
thermodynamics
and
molecular chemistry
,
enthalpy
(denoted as
H
, or specific enthalpy denoted as
h
) is a
thermodynamic property
of a
thermodynamic system
.
It can be used to calculate the heat transfer
during a
quasistatic process
taking place in a closed
thermodynamic system
under constant pressure
.
Change in enthalpy Δ
H
is frequently a more useful
value than
H
itself.
For quasistatic processes under constant pressure,
Δ
H
is equal to the change in the internal energy of the
system, plus the work that the system has done on its
surroundings.
Enthalpy
H
U W
Enthalpy Change
The heat content of a chemical system is called the
enthalpy
(symbol: H) .
The enthalpy change ( H) is the amount of heat released or
absorbed when a chemical reaction occurs at constant
pressure. H is total enthalpy, h is enthalpy per mole
h is specified per mole of substance as in the balanced
chemical equation for the reaction.
The units are usually given as kJ mol
-1
(kJ/mol) or sometimes
as kcal mol
-1
(kcal/mol).
2
1
product
reactant
phase
phase
H
H
H
for chemical reaction
H
H
H
for phase change
Latent Heat (enthalpy)
Latent Heat (enthalpy) is the "hidden" heat when a
substance absorbs or releases heat without producing a
change in the temperature of the substance, eg, during a
change of state.
Latent Heat (enthalpy) of Fusion is the heat absorbed
per mole when a substance changes state from solid to
liquid at constant temperature (melting point).
l
12
Latent Heat (enthalpy) of Vaporization is the heat
absorbed per mole when a substance changes state from
liquid to gas at constant temperature (boiling point).
l
23
Latent Heat (enthalpy) of Sublimation is the heat
absorbed per mole when a substance changes state from
solid to gas, without going through the liquid phase, at
constant temperature.
l
13
13
12
23
l
l
l
Latent Heat (enthalpy)
12
2
1
2
1
During Phase change, lets say from solid to liquid phase
at constant T and P, l
q
u w
u
u
P v
(
v
)
12
2
2
1
1
12
2
1
(
) (
)
Where h ca
l
u
pv
u
pv
l
h
h
lled the enthalp
y
23
3
2
From liquid to gas
l
h
h
13
3
1
From solid to gas
l
h
h