## Thermal Efficiency for Otto Cycle

In general the **thermal efficiency**, *η***_{th}**, of any heat engine is defined as the ratio of the work it does,

**W**, to the heat input at the high temperature, Q

_{H}.

The **thermal efficiency**, *η***_{th}**, represents the fraction of

**heat**,

**Q**

**, that is converted**

_{H}**to work**. Since energy is conserved according to the

**first law of thermodynamics**and energy cannot be be converted to work completely, the heat input, Q

_{H}, must equal the work done, W, plus the heat that must be dissipated as

**waste heat Q**

**into the environment. Therefore we can rewrite the formula for thermal efficiency as:**

_{C}The heat absorbed occurs during combustion of fuel-air mixture, when the spark occurs, roughly at constant volume. Since during an isochoric process there is no work done by or on the system, the **first law of thermodynamics** dictates *∆U = ∆Q. *Therefore the heat added and rejected are given by:

**Q _{add} = mc_{v} (T_{3} – T_{2})**

**Q _{out} = mc_{v} (T_{4} – T_{1})**

Substituting these expressions for the heat added and rejected in the expression for thermal efficiency yields:

We can simplify the above expression using the fact that the processes **1 → 2** and from **3 → 4** are adiabatic and for an adiabatic process the following p,V,T formula is valid:

It can be derived that:

In this equation, the **ratio V _{1}/V_{2}** is known as the

**compression ratio, CR**. When we rewrite the expression for thermal efficiency using the compression ratio, we conclude the

**air-standard Otto cycle**thermal efficiency is a function of

**compression ratio**and

**κ = c**

_{p}**/c**

**.**

_{v}It is very useful conclusion, because it is desirable to achieve a **high compression ratio** to extract more mechanical energy from a given mass of air-fuel mixture. A higher compression ratio permit the same combustion temperature to be reached with less fuel, while giving a longer expansion cycle. This creates more mechanical power output and **lowers the exhaust temperature**. Lowering the exhaust temperature causes the lowering of the energy rejected to the atmosphere. This relationship is shown in the figure for κ = 1.4, representing ambient air.

## Compression Ratio – Otto Engine

The **compression ratio**,** CR**, is defined as the ratio of the volume at bottom dead center and the volume at top dead center. It is a key characteristics for many internal combustion engines. In the following section, it will be shown that the **compression ratio** determines the **thermal efficiency** of used thermodynamic cycle of the combustion engine. In general, it is desired to have a high compression ratio, because it allows an engine to reach higher thermal efficiency.

For example, let assume an Otto cycle with compression ratio of CR = 10 : 1. The volume of the chamber is 500 cm³ = 500×10^{-6} m^{3} (0.5l) prior to the compression stroke. For this engine** a**ll required volumes are known:

- V
_{1}= V_{4}= V_{max}= 500×10^{-6}m^{3}(0.5l) - V
_{2}= V_{3}= V_{min}= V_{max}/ CR = 55.56 ×10^{-6}m^{3}

Note that (V_{max} – V_{min}) x number of cylinders = total engine displacement.

## Examples of Compression Ratios – Gasoline vs. Diesel

- The compression ratio in a gasoline-powered engine will usually not be much higher than
**10:1**due to potential engine knocking (autoignition) and not lower than**6:1**. - A turbocharged Subaru Impreza WRX has a compression ratio of
**8.0:1**. In general, a turbocharged or supercharged engines already have compressed air at air intake, therefore they are usually built with lower compression ratio. - A stock Honda S2000 engine (F22C1) has a compression ratio of
**11.1:1**. - Some atmospheric sportscar engines can have compression ratio up to
**12.5 : 1**(e.g. Ferrari 458 Italia). - In 2012, Mazda released new petrol engines under the brand name SkyActiv with a
**14:1**compression ratio. To reduce the risk of engine knocking, residual gas is reduced by using 4-2-1 engine exhaust systems, implementing a piston cavity, and optimizing fuel injection. - The Diesel engines have the compression ratio that normally exceed 14:1 and ratios over 22:1 are also common.

We hope, this article, **Thermal Efficiency for Otto Cycle**, helps you. If so, **give us a like** in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.