Thermodynamics:
The First Law
자연과학대학
화학과
박영동
교수
Classical thermodynamics
Thermodynamics: the first law
2.1 The conservation of energy
2.1.1 Systems and surroundings
2.1.2 Work and heat
2.1.3 The measurement of work
2.1.4 The measurement of heat
2.1.5 Heat influx during expansion
2.2 Internal energy and enthalpy
2.2.6 The internal energy
2.2.7 Internal energy as a state function
2.2.8 The enthalpy
2.2.9 The temperature variation of the enthalpy
Thermodynamic Systems, States and
Processes
Objectives are to:
•
define thermodynamics systems and states of systems
•
explain how processes affect such systems
•
apply the above thermodynamic terms and ideas to the laws of
thermodynamics
Thermodynamic universe
the system
is
the region of
interest; its region is defined by
the boundary
.
the rest of the world is its
surroundings.
The surroundings are where
observations are made on the
system.
The universe
consists of the
system and surroundings.
system
surroundings
The Universe
Various Systems
system
matter
energy
open(
열린
계
)
allowed
allowed
closed(
닫힌
계
)
forbidden
allowed
isolated(
고립
계
)
forbidden
forbidden
Some other thermodynamics terms
state,
state functions,
path, process,
extensive properties,
intensive properties.
closed
open
isolated
A State Function and Paths
The altitude is a state property, because
it depends only on the current state of
the system. The change in the value of a
state property is independent of the path
between the two states.
The distance between the initial and final
states depends on which path (as
depicted by the blue and red lines) is
used to travel between them. So it is not
a state function.
pressure, temperature, volume, ...
heat, work

Heat and work are forms of energy
transfer and
energy is conserved
.
The First Law of Thermodynamics
U
=
Q
+
W
work done
on
the system
change in
total internal energy
heat added
to system
State Function
Process Functions
Calculating the change in internal energy
We see that the person
’
s internal energy falls by 704 kJ. Later, that energy will
be restored by eating.
Suppose someone does 622 kJ of work on an exercise
bicycle and loses 82 kJ of energy as heat. What is the
change in internal energy of the person? Disregard any
matter loss by perspiration.
Solution
w
=
−
622 kJ (622 kJ is lost by doing work
on the bicycle
)
,
q
=
−
82 kJ (82 kJ is lost by heating the surroundings).
Then
the first law of thermodynamics
gives
us
U
=
q
+
w =
(

82 kJ )+ (

622 kJ) =

704 kJ
Work, and the expansion(
p

V
) work
F
F
dW
p
ex
=F/A
Increase in volume,
dV
(
p

V
work)
Work =
force
•
distance
force acting on the piston =
p
ex
×
Area
distance when expand =
dy
+y
Total Work Done
To evaluate the integral, we
must
know how the pressure
depends (functionally) on
the
volume.
We will consider the following cases
0. Constant volume work
1.
Free expansion
2.
Expansion against constant pressure
3.
Reversible isothermal expansion
0. Work for the constant volume process
For the constant volume process,
there is no
p

V
work
Heat and Internal Energy
U
=
q
+
w =
q
V
For the constant volume process,
there is no p

V work, so
If we add heat
q
to the system, the temperature
of the system increases by
T
, and the internal
energy increases by
U.
Constant volume heat capacity
Internal Energy of a Gas
A
pressurized
gas
bottle
(
V
=
0
.
05
m
3
),
contains
helium
gas
(an
ideal
monatomic
gas)
at
a
pressure
p
=
1
×
10
7
Pa
and
temperature
T
=
300
K
.
What
is
the
internal
thermal
energy
of
this
gas?
molar constant volume heat
capacity of monatomic gases
(at 1
atm
, 25
°
C)
Monatomic gas
C
V, m
(J/(
mol∙K
))
C
V, m
/
R
He
12.5
1.50
Ne
12.5
1.50
Ar
12.5
1.50
Kr
12.5
1.50
Xe
12.5
1.50
Temperature and Energy
distribution
The temperature is a parameter that
indicates the extent to which the
exponentially decaying Boltzmann
distribution reaches up into the higher
energy levels of a system. (a) When the
temperature is low, only the lower energy
states are occupied (as indicated by the
green rectangles). (b) At higher
temperatures, more higher states are
occupied. In each case, the populations
decay exponentially with increasing
temperature, with the total population of
all levels a constant.
A constant

volume bomb
calorimeter.
The constant

volume heat capacity is the
slope of a curve showing how the
internal energy varies with temperature.
The slope, and therefore the heat
capacity, may be different at different
temperatures.
1. Work for free expansion case
For the free expansion process,
there is no
p

V
work
U
=
q
+
w = q
2. Work for expansion against constant
pressure
U
=
q
+
w = q

p
V
q
p
=
U
+
p
V=
(
U
+
p V
)
If we define Enthalpy as,
H
≡
U +
pV
q
p
=
H
Enthalpy change is the heat given to the
system at constant pressure.
C
p
,
C
v
for an ideal gas
For an ideal gas,
U
and
H
do not
depend on volume or pressure.
For an example, for an ideal
monatomic gases,
U
= (3/2)
nRT
Heat capacity of CO
2
and N
2
The heat capacity with
temperature as expressed
by the empirical formula
Cp,m
/(J K

1
mol

1
) =
a
+
bT
+c
/
T
2
. The circles
show the measured
values at 298 K.
molar heat capacities,
Cp,m
/(J K

1
mol

1
) =
a
+
bT
+c
/
T
2
a
b
/(l0

3
K

1
)
c
/(10
5
K
2
)
@273K*
@298K*
@350K*
Monatomic
gases
20.78
0
0
2.50
2.50
2.50
Other
gases
Br
2
37.32
0.5

1.26
4.30
4.34
4.39
Cl
2
37.03
0.67

2.85
4.02
4.09
4.20
CO
2
44.22
8.79

8.62
4.22
4.47
4.84
F
2
34.56
2.51

3.51
3.67
3.77
3.92
H
2
27.28
3.26
0.5
3.47
3.47
3.47
I
2
37.4
0.59

0.71
4.40
4.42
4.45
N
2
28.58
3.77

0.5
3.48
3.50
3.55
NH
3
29.75
25.1

1.55
4.15
4.27
4.48
O
2
29.96
4.18

1.67
3.47
3.53
3.62
H
2
O(
l
)
75.29
0
0
9.06
9.06
9.06
C(
s
, graphite
)
16.86
4.77

8.54
0.81
1.04
1.39
*calculated results are given in unit of R(8.314 J K

1
mol

1
)
An exothermic process
When hydrochloric acid reacts with
zinc, the hydrogen gas produced
must push back the surrounding
atmosphere (represented by the
weight resting on the piston), and
hence must do work on its
surroundings. This is an example of
energy leaving a system as work.
Zn(s) + 2 HCl(aq) → ZnCl
2
(aq) + H
2
(g)
exothermic and endothermic processes
Work and Heat
Work is transfer of energy that causes or
utilizes uniform motion of atoms in the
surroundings. For example, when a
weight is raised, all the atoms of the
weight (shown magnified) move in unison
in the same direction.
Heat is the transfer of energy that causes
or utilizes chaotic motion in the
surroundings. When energy leaves the
system (the green region), it generates
chaotic motion in the surroundings
(shown magnified).
The expansion(
p

V
) Work
When a piston of area
A
moves out
through a distance
h
, it sweeps out a
volume Δ
V
=
Ah
. The external pressure
p
ex
opposes the expansion with a force
p
ex
A
.
3. Work for reversible isothermal expansion
for an ideal gas
Reversible Isothermal Expansion
Work for a perfect gas
The work of reversible, isothermal
expansion of a perfect gas. Note that for
a given change of volume and fixed
amount of gas, the work is greater the
higher the temperature.
Molecular Basis for Heat Capacity
The heat capacity depends on the
availability of levels. (a) When the levels
are close together, a given amount of
energy arriving as heat can be
accommodated with little adjustment of
the populations and hence the
temperature that occurs in the Boltzmann
distribution. This system has a high heat
capacity. (b) When the levels are widely
separated, the same incoming energy has
to be accommodated by making use of
higher energy levels, with a consequent
greater change in the ‘reach’ of the
Boltzmann distribution, and therefore a
greater change in temperature. This
system therefore has a low heat capacity.
In each case the green line is the
distribution at low temperature and the
red line that at higher temperature.
Temperature dependence of
enthalpy(H) and internal energy(U)
The enthalpy of a system increases as its temperature is raised. Note
that the enthalpy is always greater than the internal energy of the
system, and that the difference increases with temperature.
Temperature dependence of
enthalpy(H) and internal energy(U)
Note that the heat
capacityies
depend on
temperature, and that
C
p
is greater than
C
V
.
a DSC
(differential scanning calorimeter)
A
thermogram
for the protein
ubiquitin
. The protein retains its
native structure up to about 45
°
C
and then undergoes an endothermic
conformational change. (Adapted
from B.
Chowdhry
and S.
LeHarne
,
J.
Chem. Educ.
74, 236 (1997).)
sample
reference
C
p
and
C
V
The Maxwell relations
4. Work for adiabatic expansion
U
=
q
+
w =
w
U
= C
V
T=
q
ad
=
0
If
the heat capacity is
independent of temperature,
C
V
dT
=

pdV
4. Work for adiabatic expansion
For an adiabatic process for an ideal gas,
For an ideal monatomic gas
of
n
moles,
calculate
q, w,
Δ
U
for each process.
w
12
=

p
b
(
V
b

V
a
)
Δ
U
12
= C
V
(
T
2

T
1
)
= C
V
(
p
b
V
b
/
nR

p
b
V
a
/
nR
)
=
C
V
p
b
(
V
b

V
a
)
/
nR
q
12
=
Δ
U
12

w
12
T
2
=
p
b
V
b
/
nR
T
1
= T
3
=
p
b
V
a
/
nR
=
p
a
V
b
/
nR
p
b
V
a
=
p
a
V
b
w
2 3
= 0
Δ
U
23
= C
V
(
T
3

T
2
)
= C
V
(
p
b
V
a
/
nR

p
b
V
b
/
nR
)
=
C
V
p
b
(
V
a

V
b
)
/
nR
=

Δ
U
12
q
12
=
Δ
U
23
w
31
=

nRT
3
ln
(
V
a
/
V
b
) =

p
b
V
a
ln
(
V
a
/
V
b
)
Δ
U
31
=
0
q
12
=

w
31
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