**Figure 3.10:**Piston and valves in a four-stroke internal combustion engine

The actual cycle does not have the sharp transitions between the different processes that the ideal cycle has, and might be as sketched in Figure .

###

3.5.1 Efficiency of an ideal Otto cycle

The starting point is the general expression for the thermal efficiency of a cycle: The convention, as previously, is that heat exchange is positive if heat is flowing into the system or engine, so is negative. The heat absorbed occurs during combustion when the spark occurs, roughly at constant volume. The heat absorbed can be related to the temperature change from state 2 to state 3 as:
The heat rejected is given by (for a perfect gas with constant specific heats) Substituting the expressions for the heat absorbed and rejected in the expression for thermal efficiency yields We can simplify the above expression using the fact that the processes from 1 to 2 and from 3 to 4 are isentropic: The quantity is called the compression ratio. In terms of compression ratio, the efficiency of an ideal Otto cycle is:

**Figure 3.11:**Ideal Otto cycle thermal efficiency

The ideal Otto cycle efficiency is shown as a function of the compression ratio in Figure . As the compression ratio, , increases, increases, but so does . If is too high, the mixture will ignite without a spark (at the wrong location in the cycle).

###

3.5.2 Engine work, rate of work per unit enthalpy flux

The non-dimensional ratio of work done (the power) to the enthalpy flux through the engine is given by There is often a desire to increase this quantity, because it means a smaller engine for the same power. The heat input is given by where
- is the heat of reaction, i.e. the chemical energy liberated per unit mass of fuel,
- is the fuel mass flow rate.

**See also:**