Thermodynamics Cycles - Notes, Mechanical Engineering, Semester Mechanical Engineering Notes | EduRev

 Page 1


Disclaimer: The information on this page has not been checked by an independent person.   Use this 
information at your own risk. 
ROYMECH 
 
 
 
Home  
Thermos Index 
Thermodynamics Cycles 
 
 
Introduction 
Various internal combustion engine types have been devised and represented by various idealised cycles 
(otto cycle for four stroke, diesel cycle etc.. These idealised cycles are useful for determining the practical 
limitations and efficiencies possible.  They do not however provide the answer to the question.. 
 
"What is the greatest fraction of the heat transfer from a energy source is it possible to convert into work ? 
i.e. what is the limiting efficiency of conversion ?" 
 
Carnot introduced a theoretical gas cycle based on ideal reversible process which provides this information 
 
 
 
Carnot Cycle 
Carnot in 1824 arrived at the "carnot cycle" which is an idealised gas cycle that obtains the maximum 
amount of work from an engine working in a thermodynamically reversible manner.  This cycle provides a 
maximum efficiency for any thermodynamic heat engine 
 
The Carnot cycle for perfect gases is an idealised cycle composed of four reversible processes 
1. an isothermal expansion of fixed mass of gas (say in a cylinder- causing a piston to move out) 
2. an adiabetic expansion the gas (say in a cylinder- causing a piston to move out) 
3. an isothermal contraction of the gas (say in a cylinder- causing a piston to move in) 
4. an adiabetic contraction of the gas (say in a cylinder- causing a piston to move in) 
This imaginary working fluid is contained in the (cylinder)closed system and simply receives and rejects 
energy to a source and sink using perfect heat transfer (with no temperature difference ).  As a result of 
receiving and rejecting energy it expands and contracts during four ideal reversible "no-flow" 
processes.  The fluid is an ideal gas following the ideal gas laws. 
Page 2


Disclaimer: The information on this page has not been checked by an independent person.   Use this 
information at your own risk. 
ROYMECH 
 
 
 
Home  
Thermos Index 
Thermodynamics Cycles 
 
 
Introduction 
Various internal combustion engine types have been devised and represented by various idealised cycles 
(otto cycle for four stroke, diesel cycle etc.. These idealised cycles are useful for determining the practical 
limitations and efficiencies possible.  They do not however provide the answer to the question.. 
 
"What is the greatest fraction of the heat transfer from a energy source is it possible to convert into work ? 
i.e. what is the limiting efficiency of conversion ?" 
 
Carnot introduced a theoretical gas cycle based on ideal reversible process which provides this information 
 
 
 
Carnot Cycle 
Carnot in 1824 arrived at the "carnot cycle" which is an idealised gas cycle that obtains the maximum 
amount of work from an engine working in a thermodynamically reversible manner.  This cycle provides a 
maximum efficiency for any thermodynamic heat engine 
 
The Carnot cycle for perfect gases is an idealised cycle composed of four reversible processes 
1. an isothermal expansion of fixed mass of gas (say in a cylinder- causing a piston to move out) 
2. an adiabetic expansion the gas (say in a cylinder- causing a piston to move out) 
3. an isothermal contraction of the gas (say in a cylinder- causing a piston to move in) 
4. an adiabetic contraction of the gas (say in a cylinder- causing a piston to move in) 
This imaginary working fluid is contained in the (cylinder)closed system and simply receives and rejects 
energy to a source and sink using perfect heat transfer (with no temperature difference ).  As a result of 
receiving and rejecting energy it expands and contracts during four ideal reversible "no-flow" 
processes.  The fluid is an ideal gas following the ideal gas laws. 
 
 
The work done through during a complete cycle is determined using the relationships identified on 
webpage Polytropic processes.... 
 
 
From the general relationship for adiabatic polytropic processes the following relationship is 
identified. Relationships 
 
Reversible 
Process 
Heat Transfer 
at T1  
to Working 
Fluid  
From Hot 
Source 
Heat 
Rejected at 
T2 from  
Working Fluid 
From Sink 
Work done by 
working fluid 
Change in 
Internal 
Energy of 
Fluid 
Isothermal 
Expansion 
RmT 1log er 0 RmT 1log er 0 
Adiabatic 
Expansion 
0 0 
Rm(T 1 - T 2 )/ 
(1- ? ) 
-Rm(T 1 - 
T 2 )/ (1- ? ) 
Isothermal 
Compression 
0 RmT 2log er -RmT 2log er 0 
Adiabatic 
Compression 
0 0 
-Rm(T 1 - T 2 )/ 
(1- ? ) 
Rm(T 1 - T 2 )/ 
(1- ? ) 
Totals 
RmT 1log er = 
Q 1 
RmT 2log er = 
Q 2 
Rm(T 1- 
T 2 )log er= W 
0 
 
From the table it can clearly be seen that the total work done by the carnot cycle is Rm(T1 - T1 )loge r = Q1 - 
Q2.  
 
Page 3


Disclaimer: The information on this page has not been checked by an independent person.   Use this 
information at your own risk. 
ROYMECH 
 
 
 
Home  
Thermos Index 
Thermodynamics Cycles 
 
 
Introduction 
Various internal combustion engine types have been devised and represented by various idealised cycles 
(otto cycle for four stroke, diesel cycle etc.. These idealised cycles are useful for determining the practical 
limitations and efficiencies possible.  They do not however provide the answer to the question.. 
 
"What is the greatest fraction of the heat transfer from a energy source is it possible to convert into work ? 
i.e. what is the limiting efficiency of conversion ?" 
 
Carnot introduced a theoretical gas cycle based on ideal reversible process which provides this information 
 
 
 
Carnot Cycle 
Carnot in 1824 arrived at the "carnot cycle" which is an idealised gas cycle that obtains the maximum 
amount of work from an engine working in a thermodynamically reversible manner.  This cycle provides a 
maximum efficiency for any thermodynamic heat engine 
 
The Carnot cycle for perfect gases is an idealised cycle composed of four reversible processes 
1. an isothermal expansion of fixed mass of gas (say in a cylinder- causing a piston to move out) 
2. an adiabetic expansion the gas (say in a cylinder- causing a piston to move out) 
3. an isothermal contraction of the gas (say in a cylinder- causing a piston to move in) 
4. an adiabetic contraction of the gas (say in a cylinder- causing a piston to move in) 
This imaginary working fluid is contained in the (cylinder)closed system and simply receives and rejects 
energy to a source and sink using perfect heat transfer (with no temperature difference ).  As a result of 
receiving and rejecting energy it expands and contracts during four ideal reversible "no-flow" 
processes.  The fluid is an ideal gas following the ideal gas laws. 
 
 
The work done through during a complete cycle is determined using the relationships identified on 
webpage Polytropic processes.... 
 
 
From the general relationship for adiabatic polytropic processes the following relationship is 
identified. Relationships 
 
Reversible 
Process 
Heat Transfer 
at T1  
to Working 
Fluid  
From Hot 
Source 
Heat 
Rejected at 
T2 from  
Working Fluid 
From Sink 
Work done by 
working fluid 
Change in 
Internal 
Energy of 
Fluid 
Isothermal 
Expansion 
RmT 1log er 0 RmT 1log er 0 
Adiabatic 
Expansion 
0 0 
Rm(T 1 - T 2 )/ 
(1- ? ) 
-Rm(T 1 - 
T 2 )/ (1- ? ) 
Isothermal 
Compression 
0 RmT 2log er -RmT 2log er 0 
Adiabatic 
Compression 
0 0 
-Rm(T 1 - T 2 )/ 
(1- ? ) 
Rm(T 1 - T 2 )/ 
(1- ? ) 
Totals 
RmT 1log er = 
Q 1 
RmT 2log er = 
Q 2 
Rm(T 1- 
T 2 )log er= W 
0 
 
From the table it can clearly be seen that the total work done by the carnot cycle is Rm(T1 - T1 )loge r = Q1 - 
Q2.  
 
The energy supplied = RmT1 loge r = Q1. Therefore 
 
 
 
This is the maximum efficiency achievable by an reversible thermodynamic cycle working with a ideal perfect gas. 
 
The following relationship results from the above.... 
 
 
 
Air Standard cycles 
Although the Carnot cycle is theoretically the most efficient it is in no way a practical device.   Also the 
energy transfers would be far too slow for any real benefits to be realised.    Internal combustion engines 
work on non cyclic processes because the fuel-air mix enters the system and products of combustion exit 
the system.  .  However theoretical cycles based on the hypothesis that air is the working fluid in a closed 
system receiving an rejecting energy to external sinks allows provide very crude estimations on the 
theoretical efficiencies possible internal combustion engines. 
 
For the purpose of the air standard cycles the suction and exhaust strokes are not considered.T  
 
The Otto Cycle or constant volume cycle has been proposed to provide an approximation of the 4 stroke 
Internal combustion cycle designed by Otto.  The diesel cycle is used to approximate a cycle with heat 
being added at constant pressure.. 
Otto Cycle 
 
The Otto cycle is comprised of four reversible processes of air in a closed system: 
? a -> c adiabatic compression, 
 
Page 4


Disclaimer: The information on this page has not been checked by an independent person.   Use this 
information at your own risk. 
ROYMECH 
 
 
 
Home  
Thermos Index 
Thermodynamics Cycles 
 
 
Introduction 
Various internal combustion engine types have been devised and represented by various idealised cycles 
(otto cycle for four stroke, diesel cycle etc.. These idealised cycles are useful for determining the practical 
limitations and efficiencies possible.  They do not however provide the answer to the question.. 
 
"What is the greatest fraction of the heat transfer from a energy source is it possible to convert into work ? 
i.e. what is the limiting efficiency of conversion ?" 
 
Carnot introduced a theoretical gas cycle based on ideal reversible process which provides this information 
 
 
 
Carnot Cycle 
Carnot in 1824 arrived at the "carnot cycle" which is an idealised gas cycle that obtains the maximum 
amount of work from an engine working in a thermodynamically reversible manner.  This cycle provides a 
maximum efficiency for any thermodynamic heat engine 
 
The Carnot cycle for perfect gases is an idealised cycle composed of four reversible processes 
1. an isothermal expansion of fixed mass of gas (say in a cylinder- causing a piston to move out) 
2. an adiabetic expansion the gas (say in a cylinder- causing a piston to move out) 
3. an isothermal contraction of the gas (say in a cylinder- causing a piston to move in) 
4. an adiabetic contraction of the gas (say in a cylinder- causing a piston to move in) 
This imaginary working fluid is contained in the (cylinder)closed system and simply receives and rejects 
energy to a source and sink using perfect heat transfer (with no temperature difference ).  As a result of 
receiving and rejecting energy it expands and contracts during four ideal reversible "no-flow" 
processes.  The fluid is an ideal gas following the ideal gas laws. 
 
 
The work done through during a complete cycle is determined using the relationships identified on 
webpage Polytropic processes.... 
 
 
From the general relationship for adiabatic polytropic processes the following relationship is 
identified. Relationships 
 
Reversible 
Process 
Heat Transfer 
at T1  
to Working 
Fluid  
From Hot 
Source 
Heat 
Rejected at 
T2 from  
Working Fluid 
From Sink 
Work done by 
working fluid 
Change in 
Internal 
Energy of 
Fluid 
Isothermal 
Expansion 
RmT 1log er 0 RmT 1log er 0 
Adiabatic 
Expansion 
0 0 
Rm(T 1 - T 2 )/ 
(1- ? ) 
-Rm(T 1 - 
T 2 )/ (1- ? ) 
Isothermal 
Compression 
0 RmT 2log er -RmT 2log er 0 
Adiabatic 
Compression 
0 0 
-Rm(T 1 - T 2 )/ 
(1- ? ) 
Rm(T 1 - T 2 )/ 
(1- ? ) 
Totals 
RmT 1log er = 
Q 1 
RmT 2log er = 
Q 2 
Rm(T 1- 
T 2 )log er= W 
0 
 
From the table it can clearly be seen that the total work done by the carnot cycle is Rm(T1 - T1 )loge r = Q1 - 
Q2.  
 
The energy supplied = RmT1 loge r = Q1. Therefore 
 
 
 
This is the maximum efficiency achievable by an reversible thermodynamic cycle working with a ideal perfect gas. 
 
The following relationship results from the above.... 
 
 
 
Air Standard cycles 
Although the Carnot cycle is theoretically the most efficient it is in no way a practical device.   Also the 
energy transfers would be far too slow for any real benefits to be realised.    Internal combustion engines 
work on non cyclic processes because the fuel-air mix enters the system and products of combustion exit 
the system.  .  However theoretical cycles based on the hypothesis that air is the working fluid in a closed 
system receiving an rejecting energy to external sinks allows provide very crude estimations on the 
theoretical efficiencies possible internal combustion engines. 
 
For the purpose of the air standard cycles the suction and exhaust strokes are not considered.T  
 
The Otto Cycle or constant volume cycle has been proposed to provide an approximation of the 4 stroke 
Internal combustion cycle designed by Otto.  The diesel cycle is used to approximate a cycle with heat 
being added at constant pressure.. 
Otto Cycle 
 
The Otto cycle is comprised of four reversible processes of air in a closed system: 
? a -> c adiabatic compression, 
 
THERMODYNAMICS - THEORY 
 
    
Reversible and Irreversible Process 
 
 
Examples of Reversible and Irreversible 
Processes 
Click to View Movie (52 kB) 
  
A process is reversible if, after it has been carried out, 
it is possible to restore both the system and its entire 
surroundings to exactly the same states they were in 
before the process. If the system and its surroundings 
cannot return to their initial states at the end of the 
reversed process, this process is an irreversible 
process. 
A system can be restored to its initial state following a 
process, regardless if the process is reversible or not. 
If the surroundings can also be restored to its initial 
state, the process is reversible. Otherwise, the 
process is irreversible. 
Reversible process does not occur in nature. It is the 
idealization of actual process and serves as an 
idealized model to which actual process can be 
compared. 
The factors that cause a process to be irreversible are 
called irreversibilities. They include: 
? heat transfers through a finite temperature 
difference 
? unrestrained expansion of a gas 
? mixing of two gases 
? friction 
? electric current flow through a resistance 
? inelastic deformation 
? chemical reactions 
The process is irreversible if any of these effects 
present. 
      
    
Internally and Externally Reversible 
Processes 
 
 
  
When a process is carried out, irreversibilities can be 
found within the system as well as in the system's 
surroundings. A process is called internally reversible 
if the system can be restored through exactly the 
same equilibrium states which the system goes 
through. No irreversibilities occur within the 
boundaries of the system as it goes through the 
process. 
If no irreversibilities occur outside the system 
boundaries during the process, the process is called 
Page 5


Disclaimer: The information on this page has not been checked by an independent person.   Use this 
information at your own risk. 
ROYMECH 
 
 
 
Home  
Thermos Index 
Thermodynamics Cycles 
 
 
Introduction 
Various internal combustion engine types have been devised and represented by various idealised cycles 
(otto cycle for four stroke, diesel cycle etc.. These idealised cycles are useful for determining the practical 
limitations and efficiencies possible.  They do not however provide the answer to the question.. 
 
"What is the greatest fraction of the heat transfer from a energy source is it possible to convert into work ? 
i.e. what is the limiting efficiency of conversion ?" 
 
Carnot introduced a theoretical gas cycle based on ideal reversible process which provides this information 
 
 
 
Carnot Cycle 
Carnot in 1824 arrived at the "carnot cycle" which is an idealised gas cycle that obtains the maximum 
amount of work from an engine working in a thermodynamically reversible manner.  This cycle provides a 
maximum efficiency for any thermodynamic heat engine 
 
The Carnot cycle for perfect gases is an idealised cycle composed of four reversible processes 
1. an isothermal expansion of fixed mass of gas (say in a cylinder- causing a piston to move out) 
2. an adiabetic expansion the gas (say in a cylinder- causing a piston to move out) 
3. an isothermal contraction of the gas (say in a cylinder- causing a piston to move in) 
4. an adiabetic contraction of the gas (say in a cylinder- causing a piston to move in) 
This imaginary working fluid is contained in the (cylinder)closed system and simply receives and rejects 
energy to a source and sink using perfect heat transfer (with no temperature difference ).  As a result of 
receiving and rejecting energy it expands and contracts during four ideal reversible "no-flow" 
processes.  The fluid is an ideal gas following the ideal gas laws. 
 
 
The work done through during a complete cycle is determined using the relationships identified on 
webpage Polytropic processes.... 
 
 
From the general relationship for adiabatic polytropic processes the following relationship is 
identified. Relationships 
 
Reversible 
Process 
Heat Transfer 
at T1  
to Working 
Fluid  
From Hot 
Source 
Heat 
Rejected at 
T2 from  
Working Fluid 
From Sink 
Work done by 
working fluid 
Change in 
Internal 
Energy of 
Fluid 
Isothermal 
Expansion 
RmT 1log er 0 RmT 1log er 0 
Adiabatic 
Expansion 
0 0 
Rm(T 1 - T 2 )/ 
(1- ? ) 
-Rm(T 1 - 
T 2 )/ (1- ? ) 
Isothermal 
Compression 
0 RmT 2log er -RmT 2log er 0 
Adiabatic 
Compression 
0 0 
-Rm(T 1 - T 2 )/ 
(1- ? ) 
Rm(T 1 - T 2 )/ 
(1- ? ) 
Totals 
RmT 1log er = 
Q 1 
RmT 2log er = 
Q 2 
Rm(T 1- 
T 2 )log er= W 
0 
 
From the table it can clearly be seen that the total work done by the carnot cycle is Rm(T1 - T1 )loge r = Q1 - 
Q2.  
 
The energy supplied = RmT1 loge r = Q1. Therefore 
 
 
 
This is the maximum efficiency achievable by an reversible thermodynamic cycle working with a ideal perfect gas. 
 
The following relationship results from the above.... 
 
 
 
Air Standard cycles 
Although the Carnot cycle is theoretically the most efficient it is in no way a practical device.   Also the 
energy transfers would be far too slow for any real benefits to be realised.    Internal combustion engines 
work on non cyclic processes because the fuel-air mix enters the system and products of combustion exit 
the system.  .  However theoretical cycles based on the hypothesis that air is the working fluid in a closed 
system receiving an rejecting energy to external sinks allows provide very crude estimations on the 
theoretical efficiencies possible internal combustion engines. 
 
For the purpose of the air standard cycles the suction and exhaust strokes are not considered.T  
 
The Otto Cycle or constant volume cycle has been proposed to provide an approximation of the 4 stroke 
Internal combustion cycle designed by Otto.  The diesel cycle is used to approximate a cycle with heat 
being added at constant pressure.. 
Otto Cycle 
 
The Otto cycle is comprised of four reversible processes of air in a closed system: 
? a -> c adiabatic compression, 
 
THERMODYNAMICS - THEORY 
 
    
Reversible and Irreversible Process 
 
 
Examples of Reversible and Irreversible 
Processes 
Click to View Movie (52 kB) 
  
A process is reversible if, after it has been carried out, 
it is possible to restore both the system and its entire 
surroundings to exactly the same states they were in 
before the process. If the system and its surroundings 
cannot return to their initial states at the end of the 
reversed process, this process is an irreversible 
process. 
A system can be restored to its initial state following a 
process, regardless if the process is reversible or not. 
If the surroundings can also be restored to its initial 
state, the process is reversible. Otherwise, the 
process is irreversible. 
Reversible process does not occur in nature. It is the 
idealization of actual process and serves as an 
idealized model to which actual process can be 
compared. 
The factors that cause a process to be irreversible are 
called irreversibilities. They include: 
? heat transfers through a finite temperature 
difference 
? unrestrained expansion of a gas 
? mixing of two gases 
? friction 
? electric current flow through a resistance 
? inelastic deformation 
? chemical reactions 
The process is irreversible if any of these effects 
present. 
      
    
Internally and Externally Reversible 
Processes 
 
 
  
When a process is carried out, irreversibilities can be 
found within the system as well as in the system's 
surroundings. A process is called internally reversible 
if the system can be restored through exactly the 
same equilibrium states which the system goes 
through. No irreversibilities occur within the 
boundaries of the system as it goes through the 
process. 
If no irreversibilities occur outside the system 
boundaries during the process, the process is called 
externally reversible. 
A process is called totally reversible, or reversible, if it 
is both internally and externally reversible.  
      
    
The Carnot Cycle 
 
 
The Carnot Cycle (1-2): Reversible 
Isothermal Expansion 
Click to View Movie (36 kB) 
 
The Carnot Cycle (2-3): Reversible Adiabatic 
Expansion 
Click to View Movie (40 kB) 
 
The Carnot Cycle (3-4): Reversible 
Isothermal Compression 
Click to View Movie (40 kB) 
  
Heat engine operates on a cycle. The efficiency of 
heat engine depends on how the individual processes 
are executed. The most efficient cycles are reversible 
cycles, that is, the processes that make up the cycle 
are all reversible processes. 
Reversible cycles cannot be achieved in practice. 
However, they provide the upper limits on the 
performance of real cycles. 
Carnot cycle is one of the best-known reversible 
cycles. The Carnot cycle is composed of four 
reversible processes. Consider an adiabaticpiston-
cylinder device that contains gas. The four reversible 
processes that make up the Carnot cycle are as 
follows: 
? Reversible Isothermal Expansion (process 1-
2):  
Heat transfer between the heat source and 
the cylinder occurs with an infinitesimal 
temperature difference. Hence, it is a 
reversible heat transfer process. Gas in the 
cylinder expands slowly, does work to its 
surroundings, and remains at a constant 
temperature TH. The total amount of heat 
transferred to the gas during this process is 
QH. 
? Reversible adiabatic expansion (process 2-3): 
The heat source is removed, and the gas 
expands in an adiabatic manner. Gas in the 
cylinder continues to expand slowly, do work 
to its surroundings till the temperature of the 
gas drops from TH to TL. Assuming the piston 
moves frictionless and the process to be 
quasi-equilibrium, the process is reversible as 
well as adiabatic. 
? Reversible isothermal compression (process 
3-4): 
The cylinder is brought into contact with a 
heat sink at temperature TL. The piston is 
pushed by an external force and which does 
work on the gas. During the compression, the 
gas temperature maintains at TL and the 
process is a reversible heat transfer process. 
The total amount of heat rejected to the heat