# Thermal Efficiency

Written by Jerry Ratzlaff 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 Formulas

 $$\large{ \eta_{th} = \frac{ W }{ Q_H } }$$ $$\large{ \eta_{th} = \frac{ Q_H \;-\; Q_C }{ Q_H } }$$ $$\large{ \eta_{th} = 1 - \frac{ Q_C }{ Q_H } }$$

### Where:

 Units English Metric $$\large{ \eta_{th} }$$  (Greek symbol eta) = thermal efficiency $$\large{dimensionless}$$ $$\large{ W }$$ = work out $$\large{ ft-lbf }$$ $$\large{J}$$ $$\large{ Q_H }$$ = heat input $$\large{\frac{Btu}{lbm}}$$ $$\large{\frac{J}{kg}}$$ $$\large{ Q_C }$$ = waste heat $$\large{\frac{Btu}{lbm}}$$ $$\large{\frac{J}{kg}}$$