Mon May 06 12:02:08 1996:
I'm always on the look out for things that exploit the anomalies
of the immutable 'laws' of the Guardians of Status Quo. Sanjan Amin has
found a way to exploit Carnot's Cycle, what all thermal engines are
based on, in such a way than many new devices can be built. For example
a chemical free air conditioning system that uses no freon or other
CFC's as just one example... - Bob
The following Copyrighted Information (C) 1994 is posted here
with the written permission, and at the request of its author Sanjay
Amin. It may be reproduced as long as this Copyright Notice remains and
the information is reproduced intact.
The following information explains the fundamentals of the "Amin
Cycle", it comes from pages 67 to 70 (Chapter 5: "Carnot's Cycle on
Considering The Gravitational Forces Into Account") of the book "Entropy
- The key To Unlimited Resources", ISBN 0-9643037-0-1, by Sanjay Amin,
Copyright 1994.
Sadi Carnot:
Carnot's Cycle is the foundation of all devices which deal with
heat. It predicts the performance of an ideal device converting heat
energy to power or transferring heat energy from a lower temperature to
a higher temperature. It is also the foundation of all other Heat
Engine and Refrigeration Cycles. It is the foundation of the engine in
your car, the jet engine in an airplane, the engine in your lawn mower,
the machine in your refrigerator and air conditioner and also of the
power plants which drive the generators which produce electricity for
your home. Any machine which deals with the conversion of heat has to
deal with the Carnot's cycle.
The Carnot's Cycle is named after its originator, "Sadi Carnot",
who was a French engineer and physicist. In 1824 he examined the basic
problems of the operation of the steam engine: the amount of heat
supplied as compared with the work produced, the maximum amount of work
that can be produced, the suitability of water as the best medium of
power. He identified the ideal conditions in which mechanical energy
is produced from heat in a steam engine and in heat engines in general.
In spite of his intentions, Carnot's work had no practical effect on the
design of engines, but its greatest impact was on pure science,
particularly on the studies of the thermal properties of matter.
Sadi Carnot was born in Paris on June 01, 1796 and was named after
a medieval Persian poet and philosopher. Sa'di of Shiraz. The writings
of Shiraz were in vogue in Paris and Sadi's father was a member of the
five-man Directory that governed France between the Revolution and the
rise of Napoleon. In this period of unrest, the family suffered many
changes of fortune. His father fled into exile a few months after
Sadi's birth and three years later he returned and was appointed as
Napoleon's minister of war, but was soon forced to retire. A writer on
mathematics and mechanics as well as military and political matters, the
elder Carnot now had the leisure to direct his son's early education.
Sadi entered the Ecole Polytechnique in 1812, which was
considered as an institution providing a fine education and which had a
faculty of famous scientists aware of the latest developments in physics
and chemistry, which they based on a rigorous mathematics. Napoleon's
empire was being rolled back and European armies were invading France.
And soon Paris was besieged, and the students, Sadi among them, fought
a skirmish on the outskirts of the city.
Sadi remained an army officer most of his life. Friends
described him as reserved, almost taciturn, but insatiably curious about
music, science and technical progress. The mature creative period of
his life began when Sadi transferred to the recently formed General
Staff in 1819, and quickly retired on half pay, living in Paris on call
for army duty. Sadi attended public lectures on physics and chemistry
provided for workingmen. He was also inspired by long discussions with
the prominent physicist and successful industrialist Nicolas
Clement-Sesormes, whose theories he further clarified by his insight and
ability to generalize.
Sadi was always occupied with the problem on how to design good
steam engines. Steam power already had many uses then but was very
inefficient. The imports of advanced British steam engines into France
after the war with Britain showed Sadi how far French design had fallen
behind. It irked him greatly that British had progressed so far trough
the genius of a few engineers who lacked formal scientific education.
British engineers had also accumulated and published reliable data about
the efficiency of many types of engines under actual running conditions;
and they vigorously argued the merits of low and high pressure engines,
and of single-cylinder and multi-cylinder engines.
The working steam engine was constructed about 1712 by Thomas
Newcomen, a British blacksmith. Very rapidly the Newcomen engine was
installed as a power source for water pumps in coal mines throughout
Britain. It replaced cumbersome and costly horse-team-powered pumps.
The early ideas regarding the essentials of the steam engine were
very crude by today's standards. Although it is called a steam engine the
fuel being burned under the boiler actually provides the power for the
engine. Early experiments were not entirely convinced of this,
however. The power source for the steam engine was considered to be
steam and the efficiency of the engine was measured in terms of the
amount of steam it consumed. Many of these early ideas did improve the
steam engine considerably, especially those of the Scottish inventor
James Watt, who patented the first really efficient steam engine in 1769.
Watts engine was so efficient that he was able to give it away rather
than sell it directly. All the users of the engines had to pay Watt was
the money saved on fuel costs for the first three years of operation of
the engine. Watt and his partner Matthew Boulton became wealthy, and
the Industrial Revolution in England received a tremendous boost from a
new source of cheap power.
Convinced that France's inadequate development of the steam
engine technology was a factor in its downfall, Sadi began to write a
nontechnical work on the efficiency of steam engines. In his book,
Reflections on the Motive Power of Fire, published in 1824, Carnot
tackled the essence of the process of heat engines, not concerning
himself as others had done with its mechanical details.
He saw that, in a steam engine, motive power is produced when
heat drops from a higher temperature of the boiler to the lower
temperature of th e condenser, just like water when falling provides
power in a water-wheel. He worked within the framework of the caloric
theory of heat, assuming that heat was a gas which could be neither
created nor destroyed. Though the assumption was incorrect and Carnot
himself had doubts about it even while he was writing many of his
results were nevertheless true, notable the prediction that the
efficiency of an idealized engine depends only on the temperature of its
hottest and coldest parts and not on the substance (steam or any other
fluid) which drives the mechanism.
Although formally presented to the Academy of Sciences and given
an excellent review in the press, the work was completely ignored until
1834, when Emile Clapeyron a railroad engineer, quoted and extended
Carnot's results. Several factors might account for this: the number of
copies printed was limited and the dissemination of scientific
literature was slower, and such a work was hardly expected to come from
France, which was considered very backwards in steam technology.
Eventually Carnot's views were incorporated by the thermodynamic theory
as it was developed by Rudolf Clausin in Germany (1850) and William
Thomson (later Lord Kelvin) in Britain (1851).
When Carnot formulated his theory gravity was totally ignored as
the technology then was so underdeveloped that it is hard to imagine if
anyone would even think that gravity can have any subsequent impact on
the processes of the steam engine. And gravity is the leading lady of
the Amin Cycle.
Amin Cycle:
Let us analyze the Carnot's Cycle while considering the effects
of gravitational forces on the gas. In classical thermodynamics
Carnot's Cycle gives the maximum heat engine efficiency. The Carnot's
Cycle consists of two isothermal and two adiabatic processes. A
Carnot's Cycle using an ideal gas as a working substance is shown on the
Temperature-Entropy diagram in Figure 5-1. It comprises the following
steps:
(01) The gas expands isothermally at temperature T2 absorbing heat
Qh, (1-2).
(02) The gas expands adiabaticly until its temperature drops to T1,
(2-3).
(03) The gas is compressed isothermally at T1, rejecting heat Qc,
(3-4).
(04) The gas is compressed adiabaticaly back to its initial state at
temperature T2, (4-1).
Thus Qh is equal to the work done by the gas during its
isothermal expansion at temperature T2, and considering the gas to be in
a gravitation field:
[Note the formals in the book are in standard mathematical
representation, which is impossible to duplicate in a ASCII file like
this. The (^) symbol represents a SuperScript in the formals below. -
Bob]
-mgh/kT2
Qh = ne^ RT In V2/V1 (56)
2
And change in Entropy:
-mgh/kT2
S = ne^ R In V2/V1 (57)
Qh
similarly:
-mgh/kT1
Qc = ne^ RT In V4/V3 (58)
1
-mgh/kT1
= -ne^ RT In V3/V4
1
This quantity is negative because V4 is less than V3. The
ratio's of the two quantities of heat is thus:
-mgh/kT1 -mgh\kT2
Qc/Qh = (-T e^ In V3/V4) / (T -e^ In V2/V1) (59)
1 2
The equation can be simplified further by the use of the temperature
volume relations for an adiabatic process. We find for the two
adiabatic processes:
c-1 c-1
T V^ = T V^
2 2 1 3
and
c-1 c-1
T V^ = T V^
2 1 1 4
Dividing the first of these equations by the second, we find:
c-1 c-1 c-1
V^ / V^ = T V^
2 1 1 4
and
V / V = V / V
2 1 3 4
Thus the two logarithms in equation (59) are equal and the
equation reduces to:
-mgh/kT1 mgh/kT2
Qc/Qh = (-T e^ ) / (T e^ ) (60)
1 2
The efficiency of th engine is the net work divided by the heat
input and
-mh/k
E = W/Q = 1 - T / T e^ (g/T1 - g/T2) (61)
1 2
This simple results says that the efficiency of the Carnot's
engine depends not only on the temperature difference by also on the
gravitational force acting on the gas, and the Temperature-Entropy
diagram would be as shown in Figure 5-1.
The shaded area shows the decrease in entropy which is given by
the equation:
-mh/k
(1 - e^ (g/T1 - g/T2)
[The closing ")" is missing in the book - Bob]
The above Cycle is a more universal cycle as it takes the
gravitational forces into consideration and we shall hereafter call the
universal cycle the Amin Cycle.
The conventional Carnot's Cycle is a limiting case of the Amin
Cycle as when the value of g is equal to zero, "e^-0", is equal to one
and the efficiency of the Cycle is:
E = 1 - T1 / T2 (62)
Expression (62) is the efficiency given by the Carnot's Cycle.
In Science old theories are never made obsolete by new theories, they
just become subsets of the new theories which are more general and
encompass more parameters in their formulation than the theories which
become their subsets.
For example Einstein's theories are more general in applications
and they make Newton's theories a subset.; When some of the parameters
in Einstein's equations are reduced, Einstein's equations also reduce to
Newtonian equations. That is the beauty of Science, it always looks
forward acquiring ever more knowledge and understanding of the universe
we live in.
[This is my best shot at figure 5-1 in ASCII not as good as I
would like it to be. - Bob]
/|\ /|\ 1' 1 2
| T2 |-------______________________________________________
| | \ S | |
e | \ H | |
r | \ A | |
u | \ D | |
t | \ E | |
a | \ | |
r | \ I | |
e | \ N | |
p | \ | |
m | \ | |
e | \ | |
T T1 |------------------\|________________________________|
| 4 3
|
/---*-------------------------------------------------------
\ | Phi -------- Entropy ------>
\|/
FIGURE 5-1. Temperature-Entropy diagram of the Amin Cycle and
the Carnot's Cycle. (1' - 2 - 3 - 4 is the Amin Cycle) (1 - 2 - 3 -4 is
the Carnot's Cycle).
Entropy Systems Inc..
|
