ppt of Recapitulation of carnot,otto and diesel cycle, dual cycle,comparison of otto, diesel and dual cycles

1. Recapitulation of Carnot,Otto
and Diesel cycle, Dual cycle,
Comparison of Otto, Diesel
and Dual cycles
ENGINEERING THORMODYNAMICS

2. Carnot Cycle
In practice reversible cycles are unrealistic because each process is associated with
irreversibility, for example friction. However, the upper limit on the performance of
real cycles can be obtained by using the corresponding reversible cycles. And the
most well-known reversible cycle process is the Carnot cycle.
An heat engine with Carnot cycle, also called Carnot heat engine, can be simplified
by the following model:
A reversible heat engine absorbs heat QH from the high-temperature reservoir at TH
und releases heat QL to the low-temperature reservoir at TL. The temperatures TH
and TL remain unchanged. And we know from the 1st law of thermodynamics, work
is done by the heat engine, W=QH+QL. Here QH>0 and QL<0.

3. Carnot cycle

4. The Carnot cycle in this heat engine consists of two isentropic and two isothermal
processes.

5. • Process 1-2: Reversible Isothermal Expansion (TH=const)
During this process, heat is absorbed. Gas expands reversibly at the
constant temperature TH.
• Process 2-3: Reversible Adiabatic (Isentropic) Expansion
This process is isentropic. The engine is perfect insulated so that no heat is
lost and absorbed. Gas continues expanding slowly until the temperature
drops from TH to TL.
• Process 3-4: Reversible Isothermal Compression (TL=const)
After gas reaches the low temperature TL, some external force is applied on
the engine in order that gas can be compressed. Since the temperature
remains constant at TL, no change of internal energy of gas occurs, if we
assume that gas is ideal gas. Knowing from the 1st law of thermodynamics,
we obtain a conclusion that heat must be transferred from engine to low-
temperature reservoir.

6. • Process 4-1: Reversible Adiabatic (Isentropic) Compression
This process is isentropic. The engine is perfect insulated so that no heat is
lost and absorbed. Gas continues being compressed slowly until the
temperature rises from TL to TH. The process comes to an end when reaching
its initial state (state 1).

7. The thermal efficiency of the Carnot heat engine can be calculated with the general
expression:

8. From the T-s-diagramm, we obtain:
Qzu=QH=TH·ΔS1-2
Qab=QL= TL·ΔS3-4
ΔS1-2= – ΔS3-4
Therefor
This equation is also referred to as Carnot efficiency.

9. According to the Carnot efficiency, we can also draw the following conclusions:
1. The Carnot efficiency only depends on the highest and lowest temperature.
2. If we want to increase the Carnot efficiency, we can increase the highest
temperature TH or reduce the lowest temperature TL.
3. The efficiency of a Carnot heat engine is always smaller than 1. Only when
TH→∞ or TL→0 could ηth,C→1. But both methods are impossible in the practice.
4. For TH=TL we have ηth,C =0. That means, if we only one reservoir, system is not
able to undergo a cyclic process and, of course, no work can be done.
As mentioned above, the Carnot cycle is a reversible process which delivers the
most work output for a heat engine operating between the same temperature limits.
Hence, if a heat engine has the thermal efficiency of ηth, then:
• ηth < ηth,C : irreversible heat engine
• ηth = ηth,C : reversible heat engine
• ηth > ηth,C : unrealistic heat engine

10. Otto Cycle
Otto cycle is a gas power cycle that is used in spark-ignition internal combustion
engines (modern petrol engines). This cycle was introduced by Dr. Nikolaus August
Otto, a German Engineer.
• An Otto cycle consists of four processes:
1. Two isentropic (reversible adiabatic) processes
2. Two isochoric (constant volume) processes
These processes can be easily understood if we understand p-V (Pressure-Volume)
and T-s (Temperature-Entropy) diagrams of Otto cycle.

11. p-V and T-s Diagrams of Otto Cycle:

12. Processes in Otto Cycle:
As stated earlier, Otto cycle consists of four processes. They are as follows:
Process 1-2: Isentropic compression
• In this process, the piston moves from bottom dead centre (BDC) to top dead
centre (TDC) position. Air undergoes reversible adiabatic (isentropic)
compression. We know that compression is a process in which volume decreases
and pressure increases. Hence, in this process, volume of air decreases from V1 to
V2 and pressure increases from p1 to p2. Temperature increases from T1 to T2. As
this an isentropic process, entropy remains constant (i.e., s1=s2). Refer p-V and T-s
diagrams for better understanding.

13. Process 2-3: Constant Volume Heat Addition:
• Process 2-3 is isochoric (constant volume) heat addition process. Here, piston
remains at top dead centre for a moment. Heat is added at constant volume (V2 =
V3) from an external heat source. Temperature increases from T2 to T3, pressure
increases from p2 to p3 and entropy increases from s2 to s3. (See p-V and T-s
diagrams above).
In this process,
Heat Supplied = mCv(T3 – T2)
where,
m → Mass
Cv → Specific heat at constant volume

14. Process 3-4: Isentropic expansion
• In this process, air undergoes isentropic (reversible adiabatic) expansion. The
piston is pushed from top dead centre (TDC) to bottom dead centre (BDC)
position. Here, pressure decreases fro p3 to p4, volume rises from v3 to v4,
temperature falls from T3 to T4 and entropy remains constant (s3=s4). (Refer p-V
and T-s diagrams above).
Process 4-1: Constant Volume Heat Rejection
• The piston rests at BDC for a moment and heat is rejected at constant volume
(V4=V1). In this process, pressure falls from p4 to p1, temperature decreases from
T4 to T1 and entropy falls from s4 to s1. (See diagram above).
In process 4-1,
Heat Rejected = mCv(T4 – T1)
Thermal efficiency (air-standard efficiency) of Otto Cycle,

16. Diesel cycle
• Diesel cycle is a gas power cycle invented by Rudolph Diesel in the year 1897. It
is widely used in diesel engines.
• Diesel cycle is similar to Otto cycle except in the fact that it has one constant
pressure process instead of a constant volume process (in Otto cycle).
• Diesel cycle can be understood well if you refer its p-V and T-s diagrams.

17. p-V and T-s Diagrams of Diesel Cycle:

18. Processes in Diesel Cycle:
Process 1-2: Isentropic Compression
• In this process, the piston moves from Bottom Dead Centre (BDC) to Top Dead
Centre (TDC) position. Air is compressed isentropically inside the cylinder.
Pressure of air increases from p1 to p2, temperature increases from T1 to T2, and
volume decreases from V1 to V2. Entropy remains constant (i.e., s1 = s2). Work is
done on the system in this process (denoted by Win in the diagrams above).
Process 2-3: Constant Pressure Heat Addition
• In this process, heat is added at constant pressure from an external heat source.
Volume increases from V2 to V3, temperature increases from T2 to T3 and entropy
increases from s2 to s
Heat added in process 2-3 is given by
Qin = mCp(T3 − T2) kJ ………… (i)

19. Process 3-4: Isentropic Expansion
• Here the compressed and heated air is expanded isentropically inside the cylinder.
The piston is forced from TDC to BDC in the cylinder. Pressure of air decreases
from p3 to p4, temperature decreases from T3 to T4, and volume increases from V3
to V4. Entropy remains constant (i.e., s3 = s4). Work is done by the system in this
process (denoted by Wout in the p-V and T-s diagrams above).
Process 4-1: Constant Volume Heat Rejection
• In this process, heat is rejected at constant volume (V4 = V1). Pressure decreases
from P4 to P1, temperature decreases from T4 to T1 and entropy decreases from s4
to s1.
Heat rejected in process 4-1 is given by
Qout = mCv(T4 − T1) kJ ………… (ii)

20. Dual Cycle
• Dual Combustion Cycle is a combination of Otto cycle and Diesel cycle. It is
sometimes called semi-diesel cycle, because semi-diesel engines work on this
cycle. In this cycle, heat is absorbed partly at a constant volume and partly at a
constant pressure.

21. The ideal dual combustion cycle consists of two reversible adiabatic or isentropic,
two constant volume and a constant pressure processes. These processes are
represented on p-v and T-s diagrams as shown in Fig 5.13 (a) and (b) respectively.
The air standard efficiency of this cycle is given by,

22. Comparison of Otto, Diesel and Dual Cycles
The comparison of Otto, Diesel and Dual cycles can be made on the basis of compression
ratio, maximum pressure, maximum temperature, heat input, work output etc.
(a) For same compression ratio and same heat input:
• When compression ratio is kept constant process (1-2) remains the same for all the three
cycles. But process (2-3), which shows the heat addition is different for thosecycle. If
same heat is transferred in all three cycles, the temperature attained is maximum for Otto
cycle and minimum for Diesel cycle.
• The work done during the cycle is proportional to the area inside the bounded region. The
area is maximum for Otto cycle and minimum for Diesel cycle. Thus, for same heat
input, efficiency of Otto cycle will be the maximum while that of Diesel cycle will be the
minimum.

23. (b) For same maximum pressure and same heat input:
• For the same maximum pressure 3.3’. and 3” must be on same pressure line and
for the same heat input the area 2-3-a-d-2, 3’ -3’ –c-d-2 and 2”3”4” b – d – 2”
should be equal. It is obvious from figure that heat rejected by otto cycle 1-4 – a –
d – 1 is more than 1-5” – b – d – 1 and 1 – 4’ – c – d – 1.
• Since ∏thermal = Qs – QR / Qs
• The Diesel cycle is more efficient that Dual cycle, which in term is more efficient
that Otto cycle.

24. (c) For same pressure and temperature:
• It is clear from the figure that the heat rejected by all three cycles, Otto, Diesel and
Dual cycle remains the same (area 4-a – b - 1 - 4). But the heat supplied is

25. • different for all three cycles. Maximum heat is supplied during diesel cycle (area
2’-3-a-b-2’) and minimum for Otto cycle (area 2 – 3 – a – b - 2) while for Dual
cycle it is in between the two (area 2’ – 3” – 3 – a – b – 2”)
• since, ∏thermal = 1 – Heat rejected / Heat supplied
• Hence, for the above conditions the Diesel cycle is more efficient than Dual cycle,
which in turn is more efficient than Otto cycle.

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