What is meant by thermal efficiency of a heat engine?

Short Answer:

The thermal efficiency of a heat engine is a measure of how well the engine converts heat energy (from fuel) into useful mechanical work. It is expressed as a percentage and calculated by comparing the output work to the input heat energy.

Since no heat engine can convert all the input heat into work (some energy is always lost), the thermal efficiency is always less than 100%. A higher thermal efficiency means the engine is more effective in using the heat energy to produce work.

Detailed Explanation:

Thermal efficiency of a heat engine

In thermodynamics, thermal efficiency is an important concept that tells us how much useful work we get from the heat energy supplied to a heat engine. It helps us understand how efficiently a machine like a steam engine, diesel engine, or gas turbine can operate.

The basic idea is: Not all the heat supplied to an engine is converted into useful work. A part of it is always wasted—either lost to the atmosphere, cooling systems, or through friction. Thermal efficiency gives us a simple percentage to measure this performance.

Formula for Thermal Efficiency

The thermal efficiency (η) is calculated using this formula:

η = (Useful Work Output / Heat Input) × 100
Or,
η = [(Q_in – Q_out) / Q_in] × 100

Where:

  • Q_in = Heat supplied to the engine
  • Q_out = Heat rejected to the surroundings
  • Q_in – Q_out = Net work output

The result is multiplied by 100 to express it as a percentage.

Example:

Suppose a heat engine receives 1000 joules of heat energy and delivers 300 joules of mechanical work, while the rest is lost as waste heat.

Then:
η = (300 / 1000) × 100 = 30%

This means only 30% of the fuel energy is converted into work, and 70% is lost.

Factors Affecting Thermal Efficiency

  1. Type of engine or cycle used
    • Carnot engine (theoretical) has the highest possible efficiency.
    • Diesel, Otto, and Rankine cycles have different efficiencies.
  2. Temperature difference
    • Greater the difference between the heat source and sink, higher the possible efficiency.
    • According to Carnot efficiency:
      η = 1 – (T_cold / T_hot)
  3. Fuel used
    • High-energy fuels may improve efficiency.
    • Clean-burning fuels reduce heat loss.
  4. Design and material
    • Better insulation, reduced friction, and improved materials increase efficiency.
  5. Load conditions
    • Engines running under ideal load are usually more efficient.

Ideal vs Practical Efficiency

  • Carnot Efficiency:
    Theoretical maximum efficiency possible under ideal conditions.
  • Actual Efficiency:
    Real-world engines have losses due to heat, friction, and mechanical limitations, so they perform below ideal levels.

For example:

  • Steam power plant: 30–40%
  • Petrol engine: 25–30%
  • Diesel engine: 30–40%
  • Combined-cycle gas plant: up to 60%

Importance of Thermal Efficiency

  • Energy Saving: Higher efficiency means less fuel needed for the same output.
  • Cost Reduction: Less fuel = lower operational cost.
  • Environmental Benefits: Efficient engines release fewer emissions.
  • Design Improvement: Helps engineers compare and improve systems.
Conclusion

The thermal efficiency of a heat engine shows how effectively it converts the input heat energy into useful work. It is always less than 100% due to unavoidable energy losses. Understanding thermal efficiency helps engineers design better, more economical, and environmentally friendly machines. It is a key concept in power plants, automobiles, turbines, and all heat-based machines.