Adapted from “Introduction to Thermodynamics and Heat Engines” by David Mooney, “Thermodynamics” by Edward F. Obert and “Engineering Thermodynamics” by James B. Jones and George A Hawkins


When internal combustion engine operation is examined, it is seen to differ in the process of heat supply for a typical heat engine cycle because there is a permanent change in the working fluid during combustion. Therefore the fluid does not pass through a cycle so the internal combustion engine is often referred to as an "open cycle" device, not a cyclic thermodynamic heat engine.

The term "open cycle", while meaningless from a thermodynamic perspective, refers to the fact that energy is supplied to the engine from outside in the form of petroleum fuel and the unconverted portion of energy remaining in the spent combustion mixture is exhausted to the environment. “Closing the cycle”, i.e., returning the rejected products to the starting point where they can be reused, is left for nature to accomplish – hence the term “open cycle”.

An internal combustion engine is therefore a device for releasing mechanical energy from petroleum fuel using air as the working medium rather than a heat engine for processing air in a thermodynamic cycle. Heat, as such, is not supplied to the internal combustion engine, so it cannot be a heat engine in the sense described in most thermodynamic references.

A simulated heat engine cycle can be constructed to correspond approximately to the operation of an internal combustion engine by substitution of analogous heat transfer processes for some of the actual engine processes. The specific mechanism of such heat transfer is neglected because the simulation is only a theoretical model of the engine, not an actual device. Such cycles, called air standard cycles, are useful in the elementary study of internal combustion engines.

It is important to note that air standard cycles apply to the performance of an internal combustion engine because once the fuel ignites, it releases its energy as heat. If the process of combustion is ignored and the heat released is considered as heat applied during the appropriate portion of an air standard cycle, the heat conversion process in the internal combustion engine can be examined with standard thermodynamic methods.

It is equally important to remember, however, that the air standard cycle is not an internal combustion engine, so one must be careful not to carry the anology too far. Some individuals attempt to apply limitations and requirements for closed cycles to processes that are not closed. This can easily lead to an incorrect analysis of the open process because an open process by definition can gain or lose heat in the system by means that a closed cycle cannot.

Air Cycle Analysis

Studying internal combustion engine performance characteristics through use of air standard cycles involves making a number of simplifying assumptions. It involves simulating engine operation with the help of thermodynamics so as to formulate mathematical expressions which can then be solved in order to obtain the relevant information.

The method of solution will depend upon the complexity of the formulation of the mathematical expressions which in turn will depend upon the assumptions that have been introduced in order to analyze the processes in the engine. The more the assumptions, the simpler will be the mathematical expressions and the easier the calculations, but the lesser will be the accuracy of the final results.

Any device that operated in a thermodynamic cycle, absorbs thermal energy from a source, rejects a part of it to a sink and presents the difference between the energy absorbed and energy rejected as work to the surroundings is called a heat engine.

A heat engine is, thus, a device that produces work. In order to achieve this purpose, the air cycle heat engine working medium undergoes the following processes:

1. A compression process where the working medium absorbs energy as work

2. A heat addition process where the working medium absorbs energy as heat from a source.

3 An expansion process where the working medium transfers energy as work to the surroundings.

4. A heat rejection process where the working medium rejects energy as heat to a sink.

If the working medium does not undergo any change of phase during its passage through the cycle, the heat engine is said to operate in a non-phase change cycle. A phase change cycle is one in which the working medium undergoes changes of phase. Air standard cycles, using air as the working medium are examples of non-phase change cycles while the steam and vapor compression refrigeration cycles are examples of phase change cycles.

Air Standard Cycles

Since the air standard analysis is the simplest and most idealistic way of modeling an internal combustion engine, such cycles are also called ideal cycles and the engine running on such cycles are called ideal engines.

In order that the analysis is made as simple as possible, certain assumptions have to be made. These assumptions result in an analysis that is far from correct for most actual combustion engine processes, but the analysis is of considerable value for indicating the upper limit of performance. The analysis is also a simple means for indicating the relative effects of principal variables of the cycle and the relative size of the apparatus.


1. The working medium is a perfect gas with constant specific heats and molecular weight corresponding to values at room temperature.

2. No chemical reactions occur during the cycle. The heat addition and heat rejection processes are merely heat transfer processes.

3. The processes are reversible.

4. Losses by heat transfer from the apparatus to the atmosphere are assumed to be zero in this analysis.

5. The working medium at the end of the process (cycle) is unchanged and is at the same condition as at the beginning of the process (cycle).

When selecting an idealized process one is always faced with the fact that the simpler the assumptions, the easier the analysis, but the farther the result from reality. The air cycle has the advantage of being based on a few simple assumptions and of lending itself to rapid and easy mathematical handling without recourse to thermodynamic charts or tables or complicated calculations. On the other hand, there is always the danger of losing sight of its limitations and of trying to employ it beyond its real usefulness.

Equivalent Air Cycle

A particular air cycle is usually taken to represent an approximation of some real set of processes which the user has in mind. Generally speaking, the air cycle representing a given real cycle is called an equivalent air cycle. The equivalent cycle has, in general, the following characteristics in common with the real cycle which it approximates:

1. A similar sequence of processes.

2. Same ratio of maximum to minimum volume for reciprocating engines or maximum to minimum pressure for gas turbine engines.

3. The same pressure and temperature at a given reference point.

4. An appropriate value of heat addition per unit mass of air.

The Carnot Cycle

This cycle was proposed by Sadi Carnot in 1824 and has the highest possible efficiency for any cycle. The Carnot cycle, which is the basis for thermodynamic analysis of heat engines, only applies to cyclic engines that process heat in a closed cycle operating with a working fluid that is a perfect (ideal) gas. An ideal gas or perfect gas is a hypothetical gas consisting of particles of zero volume, no intermolecular forces, where the constituent particles undergo perfectly elastic collisions and are in constant random motion. Real gases do not behave this way, although the approximation is often good enough to describe real gases far from their critical points.

The thermal efficiency of the Carnot cycle is only a function of the maximum and minimum temperatures of the cycle. The efficiency will increase if the minimum temperature (or the temperature at which the heat is rejected) is as low as possible. According to this equation, the efficiency will be equal to 100% if the minimum temperature is zero, which happens to be the absolute zero temperature in the thermodynamic scale.

For optimum efficiency, the Carnot cycle (and hence the heat engine) must operate between the limits of the highest and lowest possible temperatures. In other words, the engine should take in all the heat at as high a temperature as possible and should reject the heat at as low a temperature as possible.

For the first condition to be achieved, combustion (as applicable for a real engine using fuel to provide heat) should begin at the highest possible temperature, for then the irreversibility of the chemical reaction would be reduced. Moreover, in the cycle, the expansion should proceed to the lowest possible temperature in order to obtain the maximum amount of work. These conditions are the aims of all designers of modern heat engines. The conditions of heat rejection are governed, in practice, by the temperature of the atmosphere.

It is impossible to construct a real engine which will work on the Carnot cycle. In that sense, like the air standard cycle, the Carnot cycle is but a theoretical construct useful only for analytical purposes in thermodynamics.

If such an engine were built, it would be necessary for the piston to move very slowly during the first part of the forward stroke so that it can follow an isothermal process. During the remainder of the forward stroke, the piston would need to move very quickly as it has to follow an isentropic process. This variation in the speed of the piston cannot be achieved in practice. Also, a very long piston stroke would produce only a small amount of work most of which would be absorbed by the friction of the moving parts of the engine.

Since the efficiency of the Carnot cycle is dependent only on the maximum and minimum temperatures, it does not depend on the working medium. It is thus independent of the properties of the working medium.

The Otto Cycle

The Otto cycle, which was first proposed by a Frenchman, Beau de Rochas in 1862, was first used on an engine built by a German, Nicholas A. Otto, in 1876. The cycle is also called a constant volume or explosion cycle.

An equivalent air cycle for reciprocating piston engines using spark ignition operates as folows:

At the start of the cycle, the cylinder contains a mass of air at a given pressure and volume when the piston is at its lowest position. The piston moves upward and the gas is compressed isentropically to point near the top of the stroke. At this point, heat is added at constant volume which raises the pressure to its maximum. The high pressure charge now expands isentropically, pushing the piston down, expanding to the bottom of the stroke, where the charge rejects heat at constant volume, returning to the initial state.

The isothermal heat addition and rejection processes of the Carnot cycle are replaced by constant volume processes which are theoretically more plausible, although in reality, even these processes are not practical.

In a true thermodynamic cycle, the term expansion ratio and compression ratio are synonymous. However, in a real engine, these two ratios need not be equal because of the valve timing and therefore the term expansion ratio is preferred.

The thermal efficiency of a theoretical air standard cycle simulation of an Otto cycle increases with the increase in compression ratio and specific heat ratio but is independent of the heat added and initial conditions of pressure, volume and temperature.

A plot of thermal efficiency versus compression ratio for an Otto cycle shows that the increase in efficiency is significant at lower compression ratios.

From the table below, it is seen that if:

CR is increased from 2 to 4, efficiency increase is 76%
CR is increased from 4 to 8, efficiency increase is only 32.6%
CR is increased from 8 to 16, efficiency increase is only 18.6%

  Thermal Efficiency vs Compression Ratio  
Compression Ratio (CR) Efficiency
1 0 %
2 24.2%
3 35.6 %
4 42.6 %
5 47.5 %
6 51.2 %
7 54.1 %
8 56.5 %
9 58.5 %
10 60.2 %
16 67.0 %
20 69.8 %
50 79.1 %

The Diesel Cycle

This cycle, proposed by a German engineer, Dr. Rudolph Diesel to describe the processes of his engine, is also called a constant pressure cycle In practice, the diesel engine shows a better efficiency than the Otto cycle engine because the compression of air without fuel in the former allows a greater compression ratio to be employed.

With a mixture of fuel and air, as in practical Otto cycle engines, the maximum temperature developed by compression must not exceed the self ignition temperature of the mixture; hence a definite limit is imposed on the maximum value of the compression ratio. Otto cycle engines have compression ratios in the range of 7 to 12 while diesel cycle engines have compression ratios in the range of 16 to 22.

Modern high speed diesel engines do not follow the Diesel cycle. The process of heat addition is partly at constant volume and partly at constant pressure. Such engines operate on a dual cycle.

The Dual Cycle

One of the important characteristics of real cycles is the ratio of the mean effective pressure to the maximum pressure, since the mean effective pressure represents the useful (average) pressure acting on the piston while the maximum pressure represents the pressure which chiefly affects the strength required of the engine structure.

It becomes a practical necessity to limit the maximum pressure when high compression ratios are used, as in diesel engines. This also indicates that diesel engines will have to be stronger (and hence heavier) because they must withstand higher peak pressures.

Constant pressure heat addition achieves rather low peak pressures unless the compression ratio is quite high. In a real diesel engine, in order that combustion takes place at constant pressure, fuel has to be injected very late in the compression stroke (practically at the top dead center). But in order to increase the efficiency of the cycle, the fuel supply must be cut off early in the expansion stroke, both to give sufficient time for the fuel to burn and thereby increase combustion efficiency as well as reducing after-burning and also to reduce emissions.

Such situations can be achieved if the engine was a slow speed type so that the piston would move sufficiently slowly for combustion to take place despite the late injection of the fuel. For modern high speed compression ignition engines it is not possible to achieve constant pressure combustion. Fuel is injected somewhat earlier in the compression stroke and has to go through the various stages of combustion.

Thus it is seen that early combustion is nearly at constant volume (like in a spark ignition engine). But the peak pressure is limited due to strength considerations. The rest of the heat addition after the onset of combustion is believed to take place at (or close to) constant pressure. This has led to the formulation of the dual combustion air standard cycle.

In this cycle, for high compression ratios, the peak pressure is not allowed to increase beyond a certain limit and to account for the total heat addition. The balance of the heat added is assumed to be added at constant pressure. Hence the name limited pressure cycle.

The Otto, Diesel and Dual cycle expansion process do not proceed to the lowest possible pressure, namely, atmospheric pressure. This is true of all real engines; when the exhaust valve opens, the high pressure gases undergo a violent blow-down process with consequent dissipation of available energy. This is necessary so as to allow the gases to flow out due to the pressure difference and hence reduce the piston work in driving out the gases.

The equivalent air cycle does not have these losses and therefore does not accurately reflect real engine operation. Again, one is reminded that care must be taken when modeling real engines with equivalent air cycles so as not to stray too far from the real process.