Download 03. Energy and Conservation Laws

Science about Heat
Before starting this story
You have to know
Force → Energy
Every one experiences “hotness” and “coldness”,
but how to describe it ?
Temperature and Its Measurement
• and How do we measure it ?
Galileo’s thermoscope, 1595
Thermal expansion
A digital fever thermometer use the
temperature dependence of the
electric resistance of a semiconductor
crystal to measure temperature
• Development of the temperature scales
Celsius scale 0C
(1743)
Tc  5 (TF  32)
9
Fahrenheit scale 0F
(1700)
TF  9 Tc  32
5
— Kelvin scale k, 1848
Experimental results:
A constant-volume gas thermometer
The pressure plotted as a function of
temperature for different gases. When
extended backward, the lines all intersect
temperature axis at the same point.
† absolute zero: 00k = -2730C
TK TC  273
† Can we reach the absolute zero ?
• What is temperature ?
The Zeroth Law of Thermodynamics
x
y
z
x’
y’
z’
— the physical properties (such as volume) of each object may
change right after it was placed in contact with other ones.
— as the time goes long enough, the physical properties of the
objects are no longer changing. These objects are said to
be in thermal equilibrium.
We said “They have the same temperature”.
We still haven’t answer the question: what is temperature ?
How do objects with different temperature reach
thermal equilibrium when they contact ?
— Heat flows from one object to another when there is a
different in temperature between the objects.
— Temperature is the quantity that indicates whether or
not, and in which direction, heat will flow.
what is temperature ?
What is Heat ?
Material or Motion ？
Antoine Lavoisier (1743-1794)
Joseph Black (1728-1799)
— 18 century, most people accepted a material model of heat
caloric theory of heat: heat was supposedly an invisible fluid called “caloric”
The science of thermodynamics progressed quite nicely during
this period, even though the basic concept of heat was wrong !
— Benjamin Thompson (1753-1814)
Count Rumford of Bavaria
1798, What is the source of heat that
raises the temperature of drill and
the cannon barrel ?
— 1799, Humphry Davy. melting of two ice cubes by rubbing
Where is the Caloric coming from ?
— James Joule (1810-1889)
Joule’s found that 4.19 Joul of
work was required to raise the
temperature of water by 10C
1 cal =4.2 Joul
Joule’s experiment (1840), a falling mass
turns a paddle in an insulated beaker
water in this schematic representation of
Joule’s apparatus for measuring the
temperature increase produced by doing
mechanical work on a system.
• The most important consequence in Joule’s experiment:
Heat flow is a transfer of energy
If energy is added to a system either as work or as heat, the “internal
energy” of the system increased accordingly. The change in internal
energy is equal to the net amount of heat and work transferred into
the system.
Total Energy is Conserved !
Energy Can Be Neither
Created Nor Destroyed
The First Law of Thermodynamics
Total energy is conserved !
U Q W
the change in internal
energy of the system
Note: In the macroscopic approach of thermodynamics, there is on need to
specify the physical nature of the internal energy. However, it is worth noting
that the internal energy is the sum of all possible kinds of energy “stored” in
the system.
U U ( P,V ,T ,)
state variables, thermodynamic variables
卡諾機
vs.
永動機
A model of Rumford’s cannon-boring experiments carried out at the arsenal at
Munich in 1797~8
Newcomen’s atmospheric
steam engine in 1712
James Watt’s single-acting
steam engine of 1788. The
boiler C is placed in an
outhouse. The cylinder E is kept
at a high temperature all the
time. F is the separate condenser
and H an air pump.
James Watt’s single-acting steam engine of 1788.
Industrial Revolution
— Newcomen used a steam engine to pump water from a mine in 1712
— After significant improvements made by James Watt between 1763
and 1782, the steam engine supplied the motive force for the industrial
revolution.
• What is the best efficiency that we could achieve ?
• What factors determine efficiency ?
Date
1718
1767
1774
1775
1792
1816
1828
1834
1878
1906
Builder
thermal efficiency %
Newcomen
0.5
Smeaton
0.8
Smeaton
1.4
Watt
2.7
Watt
4.5
Woolf compound engine
7.5
improved Cornish engine
12.0
improved Cornish engine
17.0
Corliss compound engine
17.2
triple-expansion engine
23.0
Sadi Carnot (1796 ~ 1832)
Sadi Carnot (1796 ~ 1832)
“Reflections on the Motive Power of Fire”, 1824
In order to consider in the most general way the principle of
production of motion by heat, it must be consider independent
of any mechanism or any particular agent. It is necessary to
establish principles applicable not only to steam engine but to
all imaginable heat-engine, whatever the working substance
and whatever the method by which it is operated.
Heat Engine
( automobile engine, diesel engine, jet engine, steam turbine,……)
Sadi Carnot & caloric theory
engine
Efficiency of a heat engine
W
e
QH
Carnot engine
An ideal engine in which all of the processes had to occur without
undue friction or departure from equilibrium. This condition means
that the engine is completely reversible.
• Efficiency of the Carnot engine
QH  QC
QC
W
ec 

1
QH
QH
QH
• Efficiency of the Carnot engine
QH  QC
QC
W
ec 

1
QH
QH
QH
The internal energy is unchanged for
one complete cycle, so the first law
gives W=Qnet.
V 
QH  nRTH ln b 
 Va 
V 
QC  nRTC ln c 
 Vd 
and we also know PV=constant for an adiabatic process
TV-1=constant ( ideal gas)
so
TH Va 1  TCVd 1
TH Vb 1  TCVc 1
Vb Vc

Va Vd
TC
e
1

Finally we obtain the efficiency of the Carnot engine c
TH
TC
the efficiency of the Carnot engine ec 1
TH
• Carnot’s theorem
1. All reversible engines operating between two given reservoirs
have the same efficiency.
2. No cyclical heat engine has a greater efficiency than a reversible
engine operating the same two temperatures.
Second Law of Thermodynamics
Kelvin’s statement (1851):
It is impossible for a heat
engine that operates in a cycle
to convert its heat input
completely into work.
impossible
heat engine
( 1824 ~ 1907 )
impossible
heat engine
Clausius’ statement (1850):
It is impossible for a cyclical
device to transfer heat continuously
from a cold body to a hot body
without the input of work or other
effect on the environment.
( 1822 ~ 1888 )
• Equivalence of the Kelvin and Clausius statement
A. if Clausius is false  Kelvin is false
B. if Kelvin is false  Clausius is false
• Proof of Carnot’s theorem
If some engine did have an efficiency greater than the
Carnot efficiency, the second law of thermodynamics would
be violated.
Ex:

e W
QH
violate Kelvin statement !
Rudolf Clausius, 1822 ~ 1888
1. Energy is conserved
2. Heat flows naturally from hot to cold.
– 1850
Carnot Engine ( Reversible Engine)
Efficiency of a heat engine
engine
Kelvin scale
QH  QC
QC
W
ec 

1
QH
QH
QH
QH Qc

TH
Tc
The ratio of heat to temperature is a constant for a
reversible process.
What about the ratio
is for an irreversible
process ?
Q
?
T
The Ratio
Q
S
T
Is called
“Entropy”
…since I think it is better to take the name of such quantities as these,
which are important for science, from the ancient language, so that
they can be introduced without change into all the modern languages,
I propose to name the magnitude S to “entropy” of the body, from
Greek word [for] a transformation. I have intentionally formed the
word entropy so as to be as similar as possible to the word energy,
since both these quantities are so nearly related to each other in their
physical significance
Rudolf Clausius, 1822 ~ 1888
1. Energy of the universe is conserved
2. The entropy of the universe tends toward a maximum
– 1865
Time Arrow
after all that…..
What is Entropy ？
Q
S
T
from Kinetic
Theory of Gas
to Statistical Thermodynamics
Ludwig Boltzmann 1844 ~ 1906