HEAT ENGINES
(Carnot Cycle)
By
M Vijaya Raju
Introduction
•In the early 19th century, steam engines became an important role in industry and transportation.
•However, a systematic set of theories of the conversion of thermal energy to motive power by steam engines had not yet been developed.
•Nicolas Léonard Sadi Carnot (1796-1832), a French military engineer, published Reflections on the Motive Power of Fire in 1824.
•The book proposed a generalized theory of heat engines, as well as an idealized model of a thermodynamic system for a heat engine that is now known as the Carnot cycle.
•Carnot developed the foundation of the second law of thermodynamics, and is often described as the "Father of thermodynamics.”
Nicolas Leonard Sadi Carnot
•He was born on 1 June 1796
Paris, France and died 24 August 1832 at the age of 36 due to cholera.
• Because of the contagious nature of cholera, many of Carnot's belongings and writings were buried together with him after his death. As a consequence, only a handful of his scientific writings survived.
•He was an eminent mathematician, military engineer and leader of the French Revolutionary Army.
Nicolas Léonard Sadi Carnot in 1813 at age of 17 in the traditional uniform
Heat Engine
• A heat engine is a device that absorbs heat (Q) and uses it to do useful work (W) on the surroundings when operating in a cycle.
• Sources of heat include the combustion of coal, petroleum or carbohydrates and nuclear reactions.
• Working substance: the matter inside the heat engine that undergoes addition or rejection of heat and that does work on the surroundings. Examples include air and water vapour (steam).
• In a cycle, the working substance is in the same thermodynamic state at the end as at the start.
Heat Engine
E
Example of a Heat Engine
Open System
The Stirling Engine
•Closed system
•Operates between two bodies with (small) different temperatures.
• Can use “stray” heat
The Stirling Cycle
= air temp.
= hot water
Heat In
Heat Out
TH >TC
(TH - TC ) is proportional to the amount of work that is done in a cycle.
Carnot Cycle
W
C
Q1
Q2
Carnot Cycle
Carnot Cycle
a
b
d
Pressure
Volume
Carnot Cycle
Carnot Cycle
We see that:
Now also
This is an important result. Temperature can be defined (on the absolute (Kelvin) scale) in terms of the heat flows in a Carnot Cycle.
What's special about a Carnot Cycle
(1) Heat is transferred to/from only two reservoirs at fixed temperatures, T1 and T2 - not at a variety of temperatures.
(2) Heat transfer is the most efficient possible because the temperature of the working substance equals the temperature of the reservoirs. No heat is wasted in flowing from hot to cold.
(3) The cycle uses an adiabatic process to raise and lower the temperature of the working substance. No heat is wasted in heating up the working substance.
(4) Carnot cycles are reversible. Not all cycles are!
What's special about a Carnot Cycle
(5) The Carnot theorem states that the Carnot cycle (or any reversible cycle) is the most efficient cycle possible. The Carnot cycle defines an upper limit to the efficiency of a cycle.
• Where T1 and T2 are the temperatures of the hot and cold reservoirs, respectively, in degrees Kelvin.
Þ As T2 > 0, hc is always <1.
Efficiency of a Stirling Engine
Question: What is the maximum possible efficiency of a Stirling engine operating between room temperature (25 °C) and boiling water (100 °C)?
Maximum efficiency would be achieved by a Carnot cycle operating between reservoirs at T1 = 373 K and T2 = 298 K.
Question: What is the maximum possible efficiency of a Stirling engine operating between room temperature (25 °C) and ice (0 °C)?
