1
The First Law of Thermodynamics
Experimentally, if we can only measure the energy entering or leaving a system,
then we can only know about
energy changes
. Therefore we re

cast the First Law
as
The change in the energy of the system
–
the internal energy change,
D
E
, is equal
to the negative of the energy change of the surroundings.
¢
U
=
energy entering

energy leaving
The First Law of Thermodynamics is a piece of accounting. We need to recognise and
account for all forms of energy entering or leaving a system.
How do we recognise energy? as
heat
and
work
.
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.:
A
A
A
A
A
A
A
2
The classical expression of the First Law
The First Law of thermodynamics is most often written in terms of the change in
the internal energy of a system as
Work is “usable energy”
–
the capacity to push a piston or a turbine, or to exert a
force,
F
, over a distance,
d
x
.
Work,
w
=
F
x
d
x
=
P
x
A
x
d
x
=
p
D
V
Which gives
Heat into the system
increases its internal
energy.
Work done by the
system decreases
its internal energy.
Where the force is
pressure x area.
Increasing volume lowers
E
int
.
3
Thermodynamics is generally concerned
with the transformation from one
Equilibrium State to another Equilibrium
State.
A transformation is called reversible if
every point along the path between the
two states is also at equilibrium.
Transformations can proceed along
different paths with the same endpoints.
The work done (by the system) and
thermal energy exchanged (between the
system and surroundings) along the
different paths may be different yet the
final states (A&B) and the final state
functions (U,P,T,v,n) are the same.
Transformations of an Ideal Gas
4
Rudolf Clausius

1850
The
first
law
of
thermodynamics
:
the
internal
energy
of
a
system
can
be
changed
by
doing
work
on
it
or
by
heating/cooling
it
.
¢
U =
q + w
The
conserved
quantity
is
not
Heat
:
The
conserved
quantity
is
Energy
which
can
be
changed
by
having
heat
flow
into/out
of
the
system
or
by
work
being
done
on/by
the
system
.
A
change
in
the
energy
of
a
system
:
Is
by
heat
leaving
or
entering
the
system
or
work
being
done
or
by
the
system
5
What is Energy
q
Internal energy
Tentative definition:
The internal energy U of a system is the sum of the kinetic
energies of all of its constituent particles, plus the sum of
all the potential energies of interactions among these
particles.
q
The first law of
thermodynamics
q
Infinitesimal changes in state
6
PV work on gasses?
Piston in a cylinder moves by
dl
due to expansion of gas at pressure
p
Force on piston:
Incremental work done:
p
7
What is Heat?
Up to mid

1800’s heat was considered a fluid
that flowed from hot objects to cold objects.
A better definition is that it is the energy that
flows from hot bodies to cold bodies in order
to establish thermal equilibrium. This is
called
thermal energy.
The term
Heat (Q)
is properly used to
describe
energy in transit
, that is thermal
energy transferred into or out of a system.
Heat only makes sense in the context of the
process of the transformation from one state
to another. It is not a
state
or equilibrium
property of the system.
8
The First Law of Thermodynamics
Thermodynamic transformations
q
is
+
if energy is
gained
by the system from the flow of heat.
q
is
–
if energy is
lost
by the system by heat flow
w
is
+
if
work
is done
on
the system.
w
is
–
if
work
is done
by
the system.
Signs for heat (
q
) and work (
w)
in thermodynamic transformations
9
Coupling between System
and Surroundings
Thermal reservoir
Adiabatic

The orange walls insulate the
system completely (no heat can pass
through)
Isochoric

Literally means no work. For
our purposes it means the Volume is
constant.
Isobaric

The force on the piston from
above is constant (for example
atmospheric pressure)
Isothermal

The thermal reservoir keeps
the system at a constant temperature
Free Expansion

The piston offers no
resistance (there is vacuum above the
brown piston)
10
Internal energy of an ideal gas
q
Free expansion
Partition is broken and gas is
Allowed to expand in an adiabatic
(no heat transfer container)
Controlled expansion
(Isothermal Reversible)
the same final state
No heat exchanged
Heat exchanged
Different paths
the same initial state
No work done
Work done
¢
U is the same for both processes (Why? What is the internal energy of an ideal gas?
11
State Variables
•
The Physical State of a system is completely
described by a small number of Macroscopic Variables
(N,V,T,U, concentrations… we will add more later on)
•
These variables are called state variables and include
pressure, volume, temperature, amount of substance,
Internal Energy
•
In a chemical reaction it is the amounts
(concentrations) of the products and reactants, their
phases (gas, liquid, solid), Temperature and Pressure.
12
a
b
c
i
f
State Functions for a Mountain
Trekker
13
Is work a state function?
P
1
P
2
V
1
V
2
•
Work on red path is w
red
=

p
2
(V
2

V
1
)
.
i
f
Ideal Gas
Work is not a state function
•
Work on blue path is w
blue
=

p
1
(V
2

V
1
)
•
Thus w
red
< w
blue
.
•
Work done on system differs for different paths from
i
to
f
.
14
•
Thermodynamics is concerned with equilbrium states.
•
An equilibrium state is one in which macroscopic properties
(E,V,P,T,n
1
,n
2
,...) do not change with time. Properties are
Either
extensive
(E,V,n) or
intensive
(T,P)
Equilibrium States
i
f
State space
15
•
Assume the contrary and take
¢
U
a
>
¢
U
b
.
•
Go forward on
a
(gaining
¢ U
a
) and backward along
b
(losing

¢
U
b
)
•
During each cycle there is a net gain in energy (
¢
E
a

¢
E
b
) > 0,
available to do work.
•
How nice! This would solve energy crisis! Perpetual motion machine!
•
Not possible, therefore,
¢
U
a
=
¢
U
b
. Energy is conserved.
•
Energy is a state function
Energy is a State Function if and only if
¢
U
a
=
¢
U
b
i
f
a
b
16
Is Heat a state function?
¢
U
is a state function but
w
is not, thus q is not a state function
.
i
f
a
b
17
Consider a transformation of an ideal gas that increases
its temperature.
Δ
U (E)
depends only on
Δ
T
18
Constant Volume Heat Capacity for Diatomic Ideal Gas
19
The First Law of Thermodynamics
Experimentally, if we can only measure the energy entering or leaving a system,
then we can only know about
energy changes
. Therefore we re

cast the First Law
as
The change in the energy of the system
–
the internal energy change,
Δ
E
, is equal
to the negative of the energy change of the surroundings.
¢
U
=
energy entering

energy leaving
The First Law of Thermodynamics is a piece of accounting. We need to recognise and
account for all forms of energy entering or leaving a system.
How do we recognise energy? as
heat
and
work
.
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.:
A
A
A
A
A
A
A
20
The classical expression of the First Law
The First Law of thermodynamics is most often written in terms of the change in
the internal energy of a system as
Work is “usable energy”
–
the capacity to push a piston or a turbine, or to exert a
force,
F
, over a distance,
d
x
.
Work,
w
=
F
x
d
x
=
P
x
A
x
d
x
=
p
D
V
Which gives
Heat into the system
increases its internal
energy.
Work done by the
system decreases
its internal energy.
Where the force is
pressure x area.
Increasing volume lowers
E
int
.
21
Thermodynamics is generally concerned
with the transformation from one
Equilibrium State to another Equilibrium
State.
A transformation is called reversible if
every point along the path between the
two states is also at equilibrium.
Transformations can proceed along
different paths with the same endpoints.
The work done (by the system) and
thermal energy exchanged (between the
system and surroundings) along the
different paths may be different yet the
final states (A&B) and the final state
functions (U,P,T,v,n) are the same.
Transformations of an Ideal Gas
22
Different paths in the
Expansion of a gas
Consider the expansion of an ideal gas with various coupling
between it (the system) and the surroundings
•
Free expansion (No external Pressure)
•
Isothermal (Constant Temperature)
•
Adiabatic (No heat transfer)
•
Isobaric (Constant pressure)
•
Isochoric (No work)
Each of these represents different coupling
Between the system and the surroundings.
Thermal reservoir
23
Free expansion
•
U = KE + PE
•
U = q + w
•
w= p
ext
dV , p
ext
=0, w=0
•
No temperature change in
surroundings so Joule measured
that q=0
•
Therefore
U =0, the internal
energy is independent of pressure
and volume and is only dependent
on Temperature
Joule originally did a free expansion experiment and concluded
that no heat was transferred between the system and its
surroundings.
24
Free expansion
•
Joule concluded that there was no
change in energy. Is this true for
an ideal gas?
•
He was clearly working on a real
gas.
•
What could have gone wrong?
Joule originally did a free expansion experiment and found
that no heat was transferred between the system and its
surroundings.
r
U
(
r
)
van der Waals
attraction
U
(
r
)
U
(
r
)
25
Joule did his experiments with relatively
dilute gases so that their behavior was
similar to an ideal gas. How would you
expect a denser gas to behave?
When thinking about this, think of the
Vanderwaals attractions between the
particles.
Would they become more or less
favorable?
If the expansion was done in an adiabatic
container what would happen? Would
the final temperature be higher, lower or
remain the same?
If the Temperature was controlled with a
bath would heat be transferred into or out
of the system?
26
Internal energy of Real Gas
Joule originally did a free expansion experiment and concluded
that virtually no heat was transferred.
However, for non

ideal gas some
temperature change occur.
The internal energy U is the sum of the
kinetic and potential
energies for all the particles that make
up the system. Non

ideal
gas have attractive intermolecular
forces. So if the internal energy
is constant, the kinetic energies
generally decrease (think of the
vanderwaals potential). Therefore as the
temperature is directly related to
molecular kinetic energy, for a non

ideal
dilute gas a free expansion results in a
drop in temperature.
r
van der Waals
interaction
U
(
r
)
What about for a dense gas?
27
Reversible Process
Pressure decreases by very small amount
Volume increases by very small amount.
Allow system to equilibrate
Remove one grain of sand at a time.
In limit of infinitesmal changes, system moves through
equilibrium states during transition

>reversible process
Grains of sand
A reversible process is one where every step of the path is at
equilibrium with its surroundings
28
Examples of Reversible and
Irreversible
•
Jumping into a pool? (from the perspective of
the water)
•
Getting into a pool slowly?
•
Free expansion of a gas
•
Isothermal expansion (piston must move very
slowly for bath)
•
Moving a glass slowly
29
Isothermal Reversible Process: T constant
: Ideal gas
For an ideal gas
Δ
U= q + w =0

w = q
30
Isothermal Reversible Process: T constant
: Ideal gas
For an ideal gas
E=q+w=0
w=

q
In rev process P
ext
=P
gas
=P=nRT/V
w=

P
1
V

P
2
V

…
31
32
33
34
Does z exist? Apply Euler’s rule of mixed differentials
35
36
37
i
f
a
b
Heat is not a State Function
Path Dependent
Inexact differentials
Can’t use
¢
Lot
’
s of paths lot
’
s of answers
Exact Differential
Path Independent
One Answer
Can use
¢
38
Joule’s Experiment
Work can be directly transformed into an equal
amount of heat through friction
Same goes for electrical work
.
How can we heat up
the water in a glass?
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