Everything about Carnot Heat Engine totally explained
A
Carnot heat engine is a hypothetical engine that operates on the reversible
Carnot cycle. The basic model for this engine was developed by
Nicolas Léonard Sadi Carnot in
1824. The Carnot engine model was graphically expanded upon by
Benoit Paul Émile Clapeyron in
1834 and mathematically elaborated upon by
Rudolf Clausius in the
1850s and
60s from which the concept of
entropy emerged.
Every thermodynamic system exists in a particular
state. A
thermodynamic cycle occurs when a
system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a
heat engine.
A heat engine acts by transferring energy from a warm region to a cool region of space and, in the process, converting some of that energy to
mechanical work. The cycle may also be reversed. The system may be worked upon by an external force, and in the process, it can transfer thermal energy from a cooler system to a warmer one, thereby acting as a
refrigerator or
heat pump rather than a heat engine.
In the adjacent diagram, from the original 1824 paper by Sadi Carnot entitled
On the Motive Power of Fire, we're told to “imagine two bodies
A and
B, kept each at a constant temperature, that of
A being higher than that of
B. These two bodies, to which we can give or from which we can remove the heat without causing their temperatures to vary, exercise the functions of two unlimited reservoirs of
caloric. We shall call the first the
furnace and the second the refrigerator.” Carnot then explains how we can obtain
motive power, for example “work”, by carrying a certain quantity of heat from the body
A to the body
B.
Modern diagram
The previous image shows the original piston-and-cylinder diagram used by Carnot in discussing his ideal engine. The figure at right shows a block diagram of a generic heat engine, such as the Carnot engine. In the diagram, the “working body” (system), a term introduced by Clausius in 1850, can be any fluid or vapor body through which
heat Q can be introduced or transmitted through to produce work. Carnot had postulated that the fluid body could be any substance capable of expansion, such as vapor of water, vapor of alcohol, vapor of mercury, a permanent gas, or air, etc. Although, in these early years, engines came in a number of configurations, typically
QH was supplied by a boiler, wherein water was boiled over a furnace;
QC was typically a stream of cold flowing water in the form of a
condenser located on a separate part of the engine. The output work
W here's the movement of the piston as it's used to turn a crank-arm, which was then typically used to turn a pulley so to lift water out of flooded salt mines. Carnot defined work as “weight lifted through a height”.
Carnot's theorem
Carnot's theorem is a formal statement of this fact:
No engine operating between two heat reservoirs can be more efficient than a Carnot engine operating between the same reservoirs.
This maximum efficiency
is defined to be:
»
at which heat is input and output, respectively. Replace
TH and
TC in Equation (1) by <
TH> and <
TC> respectively.
For the Carnot cycle, or an equivalent, <
TH> is the highest temperature available and <
TC> the lowest. For other less efficient cycles, <
TH> will be lower than
TH, and <
TC> will be higher than
TC. This can help illustrate, for example, why a
reheater or a
regenerator can improve thermal efficiency.
» See also: Heat Engine (efficiency and other performance criteria)Further Information
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