As a result of this statement, we define the **thermal efficiency**, *η***_{th}**, of any heat engine as the ratio of the work it does,

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

_{H}. The

**thermal efficiency formula**is then:

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

**heat**,

**Q**, converted

_{H}**to work**.

The **air-standard Otto cycle** thermal efficiency is a function of **compression ratio** and **κ = c**_{p}**/c**** _{v}**.

Thermal efficiency for **Diesel cycle**:

The** thermal efficiency of the Brayton cycle** in terms of the compressor **pressure ratio** (PR = p_{2}/p_{1}), which is the parameter commonly used:

The thermal efficiency of the simple **Rankine cycle** and in terms of specific enthalpies would be:

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

**heat**,

**Q**, converted

_{H}**to work**. It is a dimensionless performance measure of a heat engine that uses thermal energy, such as a steam turbine, an internal combustion engine, or a refrigerator. For refrigeration or heat pumps, thermal efficiency indicates the extent to which the energy added by work is converted to net heat output. Since it is a dimensionless number, we must always express W, Q

_{H}, and Q

_{C}in the same units.

Since energy is conserved according to the **first law of thermodynamics** and energy cannot 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 _{C}** into the environment. Therefore we can rewrite the formula for thermal efficiency as:

To give the efficiency as a percent, we multiply the previous formula by 100. Note that *η***_{th}** could be 100% only if the waste heat Q

_{C }is zero.

In general, the efficiency of even the **best heat engines** is quite low. In short, it is** very difficult** to convert thermal energy to mechanical energy. The thermal efficiencies are usually **below 50%** and often far below. Be careful when comparing it with efficiencies of wind or hydropower (wind turbines are not heat engines). There is no energy conversion between thermal and mechanical energy.[/lgc_column]

## The formula for Brayton Cycle

The thermal efficiency of simple Brayton cycle, for ideal gas and in terms of specific enthalpies can be expressed in terms of the temperatures:

## Thermal Efficiency of Rankine Cycle

The thermal efficiency of the simple Rankine cycle and in terms of specific enthalpies are:

It is very simple equation and for determination of the thermal efficiency you can use data from **steam tables**.