Thermodynamics
Heat Engine Efficiency
Efficiency of any heat engine.
Variables
ηunitless
Efficiency
Work output / Heat input
Allowed values: 0 to 1
WJ
Work output
Useful work
In SI units: kg·m²/s²
QHJ
Heat input
Heat from hot reservoir
In SI units: kg·m²/s²
Allowed values: greater than 0
QCJ
Heat output
Heat to cold reservoir
In SI units: kg·m²/s²
Derivation
η = W/Q_H. Since W = Q_H - Q_C: η = 1 - Q_C/Q_H.
Your notes
0/5000
Check value
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- W = 2 J (Work output)
- QH = 3 J (Heat input)
Result: η = 0.66666667
Where this formula is listed
- Thermodynamics formulas, under Second Law, alongside Entropy Change, Coefficient of Performance (Refrigerator), Coefficient of Performance (Heat Pump) and Clausius Inequality.
- In the thermodynamics list it comes after Carnot Efficiency and before Coefficient of Performance (Refrigerator).
- Thermodynamics formula sheet, one of 34 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Heat Engine Efficiency formula?
Heat Engine Efficiency is written η = W/Q_H = 1 − Q_C/Q_H. Efficiency of any heat engine. It belongs to Thermodynamics, under Second Law.
What are the units in η = W/Q_H = 1 − Q_C/Q_H?
In SI units, η is efficiency (dimensionless); W is work output, measured in kg·m²/s²; Q_H is heat input, measured in kg·m²/s²; Q_C is heat output, measured in kg·m²/s².
How is the Heat Engine Efficiency formula derived?
η = W/Q_H. Since W = Q_H - Q_C: η = 1 - Q_C/Q_H. The result is η = W/Q_H = 1 − Q_C/Q_H.