Thermal Efficiency Calculator
Calculate thermal efficiency for reversible (Carnot) and irreversible heat engines using fundamental thermodynamic principles
Calculate Thermal Efficiency
Calculate efficiency using heat inputs/outputs or work for real heat engines
Coal, oil, or gas fired power stations
Thermal Efficiency Results
Engine Performance Analysis
Unit Conversions
Calculation Details
Physics Analysis
Example Calculation
Steam Power Plant
Problem: Steam plant efficiency
Given:
• Heat input (Q_in) = 1000 kJ
• Heat output (Q_out) = 650 kJ
• Work output (W_net) = 350 kJ
Solution
η = W_net / Q_in = 350 / 1000
η = 0.35 = 35%
Verification: η = 1 - Q_out/Q_in = 1 - 650/1000 = 35%
Typical efficiency for steam power plants
Efficiency Formulas
Typical Efficiencies
Thermodynamics Tips
Higher temperature difference = higher Carnot efficiency
Real engines always have lower efficiency than Carnot
Combined cycles achieve highest practical efficiency
Energy balance: W_net = Q_in - Q_out
Efficiency is always less than 100% for heat engines
Understanding Thermal Efficiency
What is Thermal Efficiency?
Thermal efficiency measures how effectively a heat engine converts thermal energy into useful work. It's defined as the ratio of net work output to heat input, representing the fraction of input energy that becomes useful work rather than waste heat.
Heat Engine Fundamentals
- •Heat engines require hot and cold thermal reservoirs
- •Some heat must always be rejected (2nd Law of Thermodynamics)
- •Carnot cycle represents maximum theoretical efficiency
- •Real engines have irreversibilities that reduce efficiency
Engine Types and Applications
High Efficiency (> 45%)
Combined cycle gas turbines, large diesel engines. Use multiple thermal cycles or optimized combustion for maximum efficiency.
Medium Efficiency (25-45%)
Steam power plants, automotive engines, simple gas turbines. Practical engines with good efficiency for their applications.
Lower Efficiency (<25%)
Geothermal power, some renewable energy systems. Limited by temperature differences or thermodynamic constraints.
Note: Efficiency depends on operating conditions, fuel quality, and maintenance. Modern engines use advanced cycles to maximize efficiency.
Common Thermodynamic Cycles
Carnot Cycle
Maximum theoretical efficiency
Rankine Cycle
Steam power plants
Brayton Cycle
Gas turbine engines
Real-World Applications
Power Generation
Design and optimization of power plants. Compare different technologies and evaluate performance improvements.
Automotive Engineering
Engine performance analysis and fuel economy calculations. Optimize engine design for maximum efficiency.
Industrial Processes
Energy audits and efficiency improvements. Calculate energy costs and identify optimization opportunities.