Introduction to second law thermodynamics

1. Lecture 3
First and Second Law of
Thermodynamics

2. First Law of Thermodynamics FOR
OPEN SYSTEMS
For rate processes dividing both
sides by t and letting t0
2 2
,
( / 2 ) ( / 2 )
CV
net in
inlets ou e
CV
tl ts
m h V gz m h V g
dE
W
dt
z Q
       
 
For large processes provided all inlet/outlet conditions
are steady (not changing with time) integrate both sides
2 2
,
( / 2 ) ( / 2 )
CV net in
inlets out
CV
lets
E m h V gz m h V gz Q W
       

 
Recall enthalpy defn.:
h=u+pv
2
2
( / 2 )
( / 2 )
CV
inlets
CV
outlets
dE m u pv v gz
m u pv v gz Q W

  
   

  
 


Inserting expression for flow work
flow
outlets inlets
W pv m pv m
  
 
 
and regrouping terms

3. Conservation of mass and energy
for a steady flow process
inlet
CV
s outlets
dm
t
m
d
m 
  
2
. 2
( ) ( )
2 2
CV
CV
in out
dE
Q W m
V V
h gz h gz
m
dt
   
  
  
2 2
.
( ) (
2 2
)
CV
outlets inlets
m Q W
V V
h m
gz h gz
      
 
outlets inlets
m m

  Conservation of mass
Conservation of energ

4. Applications
 Nozzles and diffusers (e.g. jet propulsion)
 Turbines (e.g. power plant, turbofan/turbojet
aircraft engine), compressors and pumps
(power plant)
 Heat exchangers (e.g. boilers and condensers
in power plants, evaporator and condenser in
refrigeration, food and chemical processing)
 Mixing chambers (power plants)
 Throttling devices (e.g. refrigeration, steam
quality measurement in power plants)

5. Applications in pictures
Source: internet
Heat exchangers
Throttling devices

6. nozzles/diffusers
2 2
2 2
out in
out in
V V
h h 


2 2
.
( ) (
2 2
)
CV
outlets inlets
m Q W
V V
h m
gz h gz
      
 
Single stream

7. turbines
2 2
( )
2
out
cv
in
out in
V V
h Q
m W
h 

 

2 2
2
out in
out in
V V
h h

 
( )
out in
m h h Q
 
Usually
( ) 0
i
c n ou
v t
h
W m h

 

8. compressors
2 2
( )
2
out
cv
in
out in
V V
h Q
m W
h 

 

2 2
2
out in
out in
V V
h h

 
( )
out in
m h h Q
 
Usually ( ) 0
out in
cv m h h
W  
 

9. heat exchangers
, ,
( )
h h out h in
h Q
m h
  
, ,
( )
c c out c in
h Q
m h
 
, , , ,
c c out h h out c c in h h in
m h m h m h m h
  
cold (c)
hot (h)
Take CV enclosing the stream that is hot at inlet
Take CV enclosing the stream that is cold at inlet

10. Mixing chambers or “direct contact
heat exchangers”
1
2
3
 
1 1 2 2 1 2 3
m h m h m m h
  
3 1 2
m m m
  Conservation of mass
Conservation of energy

11. Principles of Thermodynamics

12. Thermal efficiency, where,
W = Net work transfer from the engine, and
Q1 = Heat transfer to engine.
Q2 = Heat transfer from cold reservoir,
1
Q
W


W
Q2
ref
(C.O.P.)
e,
performanc
of
efficient
-
Co 
W
Q1
pump
heat
(C.O.P.)
e,
performanc
of
efficient
-
Co 

13. Clausius Statement
“It is impossible for a self acting
machine working in a cyclic process
unaided by any external agency, to
convey heat from a body at a lower
temperature to a body at a higher
temperature”.
In other words, heat of, itself, cannot
flow from a colder to a hotter body

14. Kelvin-Planck Statement
“It is impossible to construct
an engine, which while
operating in a cycle produces
no other effect except to
extract heat from a single
reservoir and do equivalent
amount of work”.

16. Why does Q flow from hot to
cold?
Consider two systems, one with TA and one with TB
Allow Q > 0 to flow from TA to TB
Entropy changed by:
S = Q/TB - Q/TA
If TA > TB, then S > 0
System will achieve more randomness by exchanging
heat until TB = TA

17. Efficiencies of Engines
 Consider a cycle described by:
W, work done by engine
 Qhot, heat that flows into engine from source at
Thot
 Qcold, heat exhausted from engine at lower
temperature, Tcold
 Efficiency is defined:
Qhot
engine
Qcold
W
hot
Q
W


:
engine
hot
cold
hot
Q
Q
Q 

Since ,
hot
cold
Q
Q

1




hot
cold
hot
cold
hot
hot
cold
cold
T
T
Q
Q
T
Q
T
Q
0
/ 

 T
Q
S
hot
cold
engines
T
T

1
:


18. Carnot Engines

Idealized engine

Most efficient possible
hot
cold
hot T
T
Q
W


 1


19. Application of 2nd
law
isothermal
compression
adiabatic
expansion
isothermal
expansion
adiabatic
compression
TA
TB
1-2
2-3
3-4
4-1
Q12
Q34
W12
W23
W34
W41
Carnot
Engine
2T engine

20. Carnot Cycle

21. Efficiency of a Carnot engine
apply 1st
law for this cycle:
then energy conversion efficiency is:
for a reversible process:
A
Q
B
Q
A
Q
A
Q
W 



input
heat
work
useful

A
T
B
T
A
T
B
T
A
T
Carnot



 1

B
Q
A
Q
W 


22. Refrigerators
Qhot
engine
Qcold
W
Given: Refrigerated region is at Tcold
Heat exhausted to region with Thot
Find: Efficiency
W
Qcold


:
or
refrigerat
1
/
1




cold
hot
cold
hot
cold
Q
Q
Q
Q
Q
0
/ 

 T
Q
S
Since ,




cold
hot
cold
hot
cold
cold
hot
hot
T
T
Q
Q
T
Q
T
Q
1
/
1
:
or
refrigerat


cold
hot T
T

Note: Highest efficiency for small T differences

23. Heat Pumps
Qhot
engine
Qcold
W
Given: Inside is at Thot
Outside is at Tcold
Find: Efficiency
W
Qhot


:
pump
heat
hot
cold
cold
hot
hot
Q
Q
Q
Q
Q
/
1
1




0
/ 

 T
Q
S
Since ,




cold
hot
cold
hot
cold
cold
hot
hot
T
T
Q
Q
T
Q
T
Q
hot
cold T
T /
1
1
:
pump
heat



Like Refrigerator: Highest efficiency for small T

24. Entropy

Total Entropy always rises!
(2nd Law of Thermodynamics)

Adding heat raises entropy
T
Q
S /


Defines temperature in Kelvin!