What's going on during phase transition?
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
13
12
23
dq
du
pdv
First law
At constant volume v:
dq
v
du
v
0
v
v
v
v
v
u
c dT
du
c
T
At constant volume :
P
dq
p
du
p
pdV
p
dh
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" (ενθαλπος) meaning
"to put heat into.
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
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
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
Generalized First Law of Thermodynamics
•
Taking heat transfer to the system and work done by the
system to be positive quantities, the energy balance for a
closed system can also be expressed as:
3-29
Q W
U
KE
PE
,
Configuration
Other
W
W
W
U
m u
(
2
u
1
)
2
2
1
2
1
2
1
2
(
),
(
)
KE
m v
v
PE
mg z
z
Other
Config
Q W
W
U
KE
PE
Other
Liquid Flow
Liquid Flow (steady state)
z
2
-z
1
2
1
2
2
1
2
1
2
1
2
(
)
(
)
(
)
other
Q W
m h
h
m
mg z
z
Liquid Flow (steady state)
2
2
1
2
1
2
2
1
2
1
(
)
(
)
(
)
Heater
Q W
m h
h
m
mg z
z
??
Why
It is energy added to the SY STEM
WORK IS DONE ON THE SY STEM
If the fluid is moving a shaft then
the left hand side becomes:
heater
shaft
Liquid Flow (steady state, adiabatic
and frictionless)
Liquid Flow (steady state, adiabatic
and frictionless)
2
2
1
2
1
2
2
1
2
1
2
2
1
1
2
2
2
2
1
2
1
1
0
(
)
(
)
(
)
constant
m h
h
m
mg z
z
h
gz
h
gz
2
1
2
2
1
2
constant
constant
h
gz
u
Pv
gz
For incompressible fluid and
W=Q=0 then
u
0
2
1.
2
constant
P
gz
Example 1a:
A cylinder provided with a movable piston ( as shown ),
contains an ideal gas at T
0
, V
0
and P
0
. The cylinder wall is
made of good diathermal material. If the piston is moved
slowly until the gas final pressure is xP
0
.
Solution 1-a
1- Final Temperature is T
0
(diathermal walls).
0
0
0
0
2
P V
f
f
PV
xPV
f
V
f
V
/
x
3
U
f nR T
/ 2
0
4
Q
U W
Q W
0 0
0 0 0 0
5
ln
ln
f f
V V
V V
dV
W
PdV
nRT
nRT
x
PV
x
V
0
0
Example 1-b
The same as problem 1-a but the external pressure on the
piston increased or decreased suddenly up to xP
0
.
1- Final Temperature is T
0
(diathermal walls).
0
0
0
0
2
P V
f
f
PV
xPV
f
V
f
V
/
x
3
U
f nR T
/ 2
0
4
Q
U
W
by
Q
W
by
W
on
0
0
Example 1-c
The same as problem 1-a but the walls are adiabatic the gas
has constant
the external pressure on the piston increased
or decreased slowly up to xP
0
.
1- Final Temperature
T
0
(adiabatic walls).
1
0
0
0
0
2
P V
f
f
PV
xPV
f
V
f
x V
0
0
0
1
1
1
0
0
0
0
0
3
f
f
f
f
f
f
f
PV
P V
nRT
T
T
P V
T
T
x
T
x
T
PV
Example 1-
c Cont……
4
Q
U
W
,
Q
0
Adiabatic process
U
W
1
0
0
1
0
0
5
(
)
(
1)
1
1
(
1)
1
f
nRT
nR
W
T
T
x
Example 1-d
The same as problem 1-c the walls are adiabatic the gas has
constant
the external pressure on the piston increased or
decreased suddenly up to xP
0
.
1
,
0
by
on
Q
U W
Q
adiabatic process
U
W
W
0
0
0
0
0
2
W
on
xP V
(
V
f
)
xPV
P V
f
f
nR xT
(
T
f
)
0
0
2
1
3
U
f
nR T
(
f
T
)
nR
(
T
f
T
)
W
on
0
0
1
4
nR
(
T
f
T
)
nR xT
(
T
f
)
0
1
5
T
f
x
x
T
Example 1-
d Cont…….
0 0 0
0
0
1
(
1)
6
W
by
U
nR
(
T
f
T
)
T
P V
(
T
f
T
)
0 0
0
0
0
1
(
1)
by
PV
x
x
W
U
T
T
T
0 0
(
1)(
1)
(
1)
by
PV
x
W
U
Example 2-a
A cylinder provided with a movable
piston ( as shown ), contains an ideal
gas at T
0
, V
0
and P
0
. The cylinder wall
is made of good diathermal material. If
the piston is moved slowly until the gas
final pressure is xP
0
.Note that the
cylinder is
vertical
and we must take
into account the changes in the
gravitational potential energy
of
the system.
Example 2-
a Cont…….
1- Final Temperature is T
0
(diathermal walls).
0
0
0
0
2
P V
f
f
PV
xPV
f
V
f
V
/
x
2
1
4
0
gas
(
) 0
Q
U W
PE
KE
Q
W
m
g z
z
0 0
0 0 0 0
3
ln
ln
f f
V V
V V
dV
W
PdV
nRT
nRT
x
PV
x
V
0
1
The same as example 2-a but the pressure on the piston
increased suddenly to xP
0
.
Example 2-b
1- Final Temperature is T
0
(diathermal walls).
0
0
0
0
2
P V
f
f
PV
xPV
f
V
f
V
/
x
0
0
0
0
3
W
by
W
on
xP V
(
f
V
)
PV x
(
1)
2
1
4
0
gas
(
) 0
Q
U W
PE
KE
Q
W
m
g z
z
0
0 0 0 0 0
1
5
Q
PV x
(
1)
m
gasg
V
fV
PV x
(
1)
m
gasgV
x
A
Ax
Example 2-c
The same as example 2-a but the cylinder wall is adiabatic
and the pressure on the piston increased slowly to xP
0
.
1
(
)
(
)
0
1
gas
d Q
dU
dW
d PE
d KE
m
g
nR
dT
PdV
dV
A
2
nRT
PV
nRdT
PdV
VdP
3
0
1
gas
m
g
PdV
V dP
PdV
dV
A
Example 2-
c Cont………
4
0
(
1)
gas
dP
dV
m
g
V
P
A
0
0
5
P
f
(
1)
mg A V
/
f
P
(
1)
mg A V
/
1
0
0
0
(
1)
/
6
(
1)
/
f
P
mg A
V
V
xP
mg A
1
0
0
0
0
0
0
(
1)
/
7
(
1)
/
f
f
f
P
mg A
P V
T
T
x
T
PV
xP
mg A
Example 2-
c Cont………
8
(
)
(
)
0
1
gas
d Q
dU
dW
d PE
d KE
m
g
nR
dT
dW
dV
A
0
0
9
1
(
)
(
)
1
gas
gas
f
f
f
f
m
g
nR
dW
dT
dV
A
m
g
nR
W
T
T
V
V
A
Example 2-d
The same as example 2-a but the
cylinder wall is adiabatic
and the pressure on the piston increased
suddenly
to xP
0
.
0
0
1
(
)
(
)
0
(
)
(
)
1
gas
on
f
f
Q
U
W
PE
KE
m
g
nR
T
T
W
V
V
A
0
0
2
W
on
xP V
(
V
f
)
0
0
0
0
0
0
0
3
0
(
)
(
)
(
)
1
0
(
)
(
)
1
gas
f
f
f
gas
f
f
m
g
nR
T
T
xP V
V
V
V
A
m
g
nR
T
T
xP
V
V
Example 2-
d Cont……
0
0
0
4
0
(
)
(
)
1
gas
f
f
m
g
nR
T
T
xP
V
V
A
0
0
0
0
0
0
0
0
5
f
f
f
f
f
f
1
f
PV
P V
T
T
V
V
V
V
V
T
T
xT
xT
0
0
0
0
0
0
6
0
(
)
1
1
gas
f
f
gas
f
f
m
g
T
nR
T
T
xP
V
A
xT
m
g
PV
T
T
Example 2-
d Cont……
0
0
0
[
1]
(
1)
(
1)
gas
f
gas
xP A x
x
m
g
T
T
xP A
m
g
0
0
0
0
0
0
7
0
1
1
(
1)
gas
f
m
g
f
PV
T
T
xP
V
T
A
xT
0 0
0 0 0 0
0 0 0 0
0
(
1)
(
1)
gas gas
f
PV
m
gV
PV
m
gV
T
PV
xPV
T
xA
A
0
0
0
1
(
1)
(
1)
(
1)
gas
gas
f
m
g
m
g
T
x
T
xP A
xP A
Example 2-
d Cont……
0
0
f
f
T
V
V
xT
0
(
0
)
on
f
W
xP V
V
0
0
0
[
1]
(
1)
(
1)
gas
f
gas
xP A x
x
m
g
V
V
x
xP A
m
g