Entropy and
the Second Law of
Thermodynamics
MECH3400
The essence of the
2
nd
law
1
st
law:
allows for prediction of change
of state due to energy transfer
does not point the direction of
time
does not reveal the possibility or
impossibility for a process to
occur
2
nd
law helps, as entropy:
never decreases for an isolated
system
indicates the possibility for a
process to occur
is a “signpost of time”
2
nd
law:
Entropy
is a single macroscopic
property which measures:
microscopic disorder
(randomness)
uncertainty (probability) to
determine the microscopic
state
unavailability of internal
energy
Example: mixing
......
diffusion

“random walk”
Entropy and
temperature
experience says that
temperature is:
an indication of the direction of
energy transfer as heat
a property that two systems have
in common when in (thermal)
equilibrium
in microscopic terms

associated with the energy of the
molecules
now a thermodynamic
definition of temperature
Entropy and
temperature
(continued)
2nd law suggests
that at equilibrium
S=S
max
:
Q
A
B
rigid
wall
insulating
rigid wall
Entropy and
temperature
(continued)
at equilibrium:
Entropy and
temperature
(continued)
thermodynamic definition of temperature:
Entropy and
temperature
(continued)
in order to ensure
dS>0
for A and B identical
Entropy and
pressure
mechanics says that
pressure is:
force per unit area exerted by
matter on its boundaries
a property that two systems have
in common when in
(mechanical) equilibrium
in microscopic terms

associated with molecular
collisions with a “wall”
now a thermodynamic
definition of pressure
Entropy and
pressure
(continued)
at equilibrium:
Q
A
B
insulating
rigid wall
W
Entropy and
pressure
(continued)
gives thermal equilibrium:
gives mechanical equilibrium:
Entropy and
pressure
(continued)
thermodynamic definition of pressure:
Gibbs equation
Reversible and
irreversible processes
reversible process:
“produces” no entropy
“backward” process possible
“leaves no footprints in the sand
of time”
uncommon
irreversible process:
“produces” entropy
“backward” process impossible
increases the “disorganised”
energy on the expense of
“organised” energy
common
Some reversible
processes
pneumatic spring
frictionless motion
Some other (nearly)
reversible processes
restrained compression or
expansion
heat transfer due to a
infinitesimal temperature
difference
magnetisation, polarisation
electric current flow through
a zero resistance
restrained chemical reaction
mixing of two identical
substances at the same state
Some irreversible
processes
motion with friction
spontaneous
chemical reaction
.....
.
mixing
heat transfer
T
1
> T
2
Q
unrestrained
expansion
P
1
> P
2
Ideal reservoirs

TER
Thermal Energy Reservoir
(TER)
TER is a fixed mass that can
undergo only heat interactions
with its environment
heat transfer to/from TER will
alter its internal energy
TER has uniform and constant
internal temperature
TER is always in equilibrium
TER is a source or sink of
“disorganised” energy
example: large block of copper
Ideal reservoirs

MER
Mechanical Energy Reservoir
(MER)
MER is a system that possesses
energy only in a fully organised
mechanical form such as raising
of a weight
the only energy transfer for a
MER is reversible work
all motions within MER are
frictionless so that work input
can be completely recovered
MER is a source or sink of
“organised” energy
example: dead weight on the end
of a frictionless pulley
Entropy change for
a TER and a MER
0
Gibbs equation:
1
st
law:
for a TER:
and for a MER:
2
nd
law:
Entropy change
for a control mass
C
TER
T
MER
W
Q
CM
T
for control mass
Q
is energy input
0
2
nd
law:
Entropy change
for a control mass (cont.)
for reversible process
in a control mass
Q
is energy input
useful in measurements
for adiabatic process
which is reversible
in a control mass
only mode of energy
transfer is work
eg adiabatic
compression
Entropy flow and
production
irreversible process
reversible process
impossible process
for a
control mass:
2
nd
law:
Entropy change
for a control volume
Q
2
W
shaft
v
1
v
2
dE
CM
A
B
1
2
v
1
dt
v
2
dt
assume: fixed boundaries, 1

D
transient (non

steady state) flow
Control volume and simultaneously
control mass at time
t
Control mass boundary at time
t+dt
Q
1
Q
3
2
nd
law:
Entropy change
for a control volume
from control mass to control volume
using Reynolds transport theorem:
......
now from the 2
nd
law for the control mass:
2
nd
law:
Entropy change
for a control volume
to the 2
nd
law for the control volume:
2
nd
law:
Entropy change
for a control volume
2
nd
law in the rate form:
Application of 2
nd
law to
energy conversion systems
isothermal
compression
adiabatic
expansion
isothermal
expansion
adiabatic
compression
T
A
T
B
1

2
2

3
3

4
4

1
Q
12
Q
34
W
12
W
23
W
34
W
41
Carnot
Engine
2T engine
Application of 2
nd
law to
energy conversion systems
Carnot
Cycle
T
A
T
B
1
2
3
4
T
A
T
B
1
2
3
4
V
V
T
T
reversible
heat engine
reversible
heat pump
R2T engine
Application of 2
nd
law to
energy conversion systems
for a cycle no change in CV so:
for a reversible process:
for an irreversible process:
Efficiency of a
Carnot engine
apply 1
st
law for this cycle:
then energy conversion efficiency is:
for a reversible process:
Efficiency of an
irreversible engine
for an irreversible process:
2
nd
law

other formulations
Kelvin

Planck statement:
“continuously operating 1T
engine is impossible”
Clausius statement:
“a zero

work heat pump is
impossible”
www
Pressure
thermodynamic = mechanical
Gibbs:
1st law:
for a reversible process
for an equilibrium state
compression:
Entropy for ideal gasses
GENERALLY:
S = N s(T,P)
where N is the number of moles
FOR IDEAL GASSES:

Standard Pressure (1atm)

Standard Pressure entropy
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