# Thermal Efficiency

on . Posted in Thermodynamics

Thermal efficiency, abbreviated as $$\eta_{th}$$ (Greek symbol eta), a dimensionless number, is the fraction of heat that is converted to work or desired output divided by required input.  Thermal efficiency is a measure of how effectively a device or system converts thermal energy into useful work or other desired outputs.  It is a ratio of the useful output or work to the input thermal energy.  The heat input represents the total amount of heat energy supplied to the engine, and the useful work output is the work done by the engine.  The thermal efficiency indicates the proportion of the input heat energy that is converted into useful work.

In the case of power plants or other energy conversion systems, thermal efficiency is often expressed as the ratio of the net electrical power output to the heat input.  It is a measure of how efficiently the system converts heat energy into electrical power.

Thermal efficiency is influenced by factors such as the design and operating characteristics of the device or system, the properties of the working fluid or substance, and the temperature difference between the heat source and the heat sink.  It is important to note that no heat engine or energy conversion system can achieve 100% thermal efficiency due to various thermodynamic limitations, such as losses in the form of heat transfer to the surroundings or internal irreversibilities.  The efficiency of real world systems is always less than the theoretical maximum, as defined by the Carnot efficiency.

### Thermal efficiency Formula

$$\eta_{th} \;=\; ( W_o \;/\; Q_i ) \; 100$$     (Thermal Efficiency)

$$W_o \;=\; \eta_{th} \; Q_i \;/\; 100$$

$$Q_i \;=\; W_o \; 100 \;/\; \eta_{th}$$

Symbol English Metric
$$\eta_{th}$$  (Greek symbol eta) = thermal efficiency $$dimensionless$$
$$W_o$$ = output work  $$ft-lbf$$ $$J$$
$$Q_i$$ = input heat $$Btu \;/\; lbm$$  $$kJ \;/\; kg$$