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

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%
Thermal Efficiency

Engine Performance Analysis

Calculated Efficiency:0.00%
Typical Steam Turbine Power Plant Range:30-45%

Unit Conversions

%
0.000000
decimal
0.000000
fraction
0 / 1

Calculation Details

Thermal Efficiency Formulas:
• η = W_net / Q_in (work-based)
• η = 1 - Q_out / Q_in (heat-based)
Energy Balance: W_net = Q_in - Q_out
Q_in = 0 J
Q_out = 0 J
W_net = 0 J

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

η = W_net / Q_in
Work-based Formula
η = 1 - Q_out / Q_in
Heat-based Formula
η = 1 - T_c / T_h
Carnot (Reversible)
η = Thermal efficiency
W_net = Net work output
Q_in = Heat input
Q_out = Heat output
T_h, T_c = Hot/cold temperatures

Typical Efficiencies

Combined Cycle50-60%
Diesel Engine35-45%
Steam Turbine30-45%
Nuclear Plant32-37%
Gasoline Engine25-35%
Gas Turbine25-40%
Real-world efficiency ranges

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

η = 1 - T_c/T_h

Maximum theoretical efficiency

Rankine Cycle

η = 1 - q_out/q_in

Steam power plants

Brayton Cycle

η = 1 - 1/r_p^(k-1)/k

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.