Carnot Cycle and Engine Efficiency

1. CARNOT
ENGINE

2. Nicolas Léonard Sadi Carnot was a French
mechanical engineer in the French Army, military
scientist and physicist, and often described as the
"father of thermodynamics".
Carnot discovered that a steam engine works, not by
consuming caloric, but by transferring heat from a
warm reservoir to a cool one, using part of the heat to
produce work. The greater the temperature difference
between the two reservoirs, the more efficient the
engine.

3. CARNOT ENGINE
Carnot engine is an ideal heat engine whose efficiency is maximum.
In carnot engine, carnot cycle is used.
In carnot engine, ideal gas is the working substance and all the
dissipative forces are absent.

4. CARNOT CYCLE
Carnot devised an ideal cycle of operation for a heat engine and is
know as carnot cycle.
In one complete cycle of operation there are four different
thermodynamic processes.

5. 4 PROCESSES OF CARNOT
CYCLE

6. ISOTHERMAL EXPANSION
At first, the working substances is kept in contact with the source. The
piston of the cylinder is moved outwards. The gas expands at constant
temperature. The amount of heat (𝑄1) is absorbed from the source to make
the temperature constant. The volume increases and pressure decreases.
V P

7. ADIABATIC EXPANSION
The lower conducting side of the cylinder is kept in contact with the
insulating outwards. The piston of the cylinder is moved outwards. The gas
expands such that no heat enters the system or leaves from it. The
temperature and pressure decreases. The temperature is decreased from
𝑇1𝑡𝑜 𝑇2.
V P T

8. ISOTHERMAL COMPRESSION
The cylinder is kept in contact with the sink. The piston of the cylinder is
moved inwards. The gas is compressed at constant temperature. The excess
heat produced (𝑄2) will flow to the sink to make the temperature constant.
The volume decreases and pressure increases.
V P

9. ADIABATIC COMPRESSION
The cylinder is kept in contact with the insulating stand. The piston of the
cylinder is moved inwards. The gas is compressed such that no heat enters
the system or leaves from it. The volume decreases and pressure increases.
The temperature remain constant.
V P

11. ENGINE
EFFICIENCY

12. Efficiency of Carnot Engine
We have the efficiency of heat engine,
𝜂 = 𝑊/𝑄ℎ
where “W” is the work done and 𝑄ℎ is the amount of heat absorbed from
the source.
Also 𝑊 = 𝑄ℎ − 𝑄𝑐 is the amount of energy rejected to sink.
There fore, 𝜂 =
𝑄ℎ−𝑄𝑐
𝑄ℎ
= 1 − (
𝑄𝑐
𝑄ℎ
)
For carnot engine, it can be shown that:
𝜂 = 1 − (
𝑇𝑐
𝑇ℎ
) where 𝑇ℎ is the temperature of source and 𝑇𝑐 that of sink

13. Important results:
 η is always less than 1 because TH is less than TC. This implies the
efficiency cannot be 100%. It can be 1 or 100% only
when TC = 0K (absolute zero of temperature) which is impossible to
attain practically.
The efficiency of the Carnot’s engine is independent of the working
substance. It depends only on the temperatures of the source and the
sink. The greater the difference between the two temperatures,
higher the efficiency.
When TC=TH the efficiency η =0. No engine can work having source
and sink at the same temperature.

14. Example
1. For a coal-fired utility boiler, the temperature of high
pressure steam (Thot)would be about 540°C and Tcold,
the cooling tower water temperature, would be about
20°C. Calculate the Carnot efficiency of the power
plant.

16. Example
2. A steam engine boiler is maintained at 250°C and
water is converted into steam. This steam is used to do
work and heat is ejected to the surrounding air at
temperature 300K. Calculate the maximum efficiency it
can have?

19. TEST I (10 points)
1. What is a working fluid in Carnot’s cycle(5 points)
2. What is a Carnot heat engine? (5 points)
3. Name the processes involved in the Carnot cycle?
(5 points)

20. TEST II (5 points)
There are two Carnot engines A and B operating in
two different temperature regions. For Engine A the
temperatures of the two reservoirs are 150°C and
100°C. For engine B the temperatures of the reservoirs
are 350°C and 300°C. Which engine has lesser
efficiency?

21. ANSWERS:
1. The working fluid in a Carnot’s cycle is an ideal gas.
2. Carnot heat engine is a theoretical engine that operates on a
reversible carnot cycle. It has maximum efficiency that a heat
engine can possess.
3. (1)Isothermal Expansion
(2)Adiabatic Expansion
(3)Isothermal Compression
(4)Adiabatic Compression