A heat engine is a thermodynamic system that operates in a cyclic manner to convert thermal energy (heat) into mechanical energy (work). It absorbs heat from a high-temperature source, converts a fraction of this heat into useful work, and rejects the remaining energy to a low-temperature sink.
Essential Components of a Heat Engine
Every heat engine requires three fundamental components to perform continuous work:
- Source (Hot Reservoir): A thermal reservoir maintained at a constant high temperature (T1). It has infinite thermal capacity, meaning heat can be extracted from it without lowering its temperature.
- Working Substance: The material inside the engine that undergoes thermodynamic changes (such as expansion and compression) to perform work. Examples include a mixture of fuel vapor and air in internal combustion engines, or steam in a steam turbine.
- Sink (Cold Reservoir): A thermal reservoir maintained at a constant lower temperature (T2). It has infinite thermal capacity, allowing it to absorb waste heat from the working substance without experiencing a temperature rise.
Thermodynamic Cycle and Efficiency
The Energy Balance
During each complete cycle of operation, the working substance absorbs a quantity of heat (Q1) from the source, performs a net amount of external mechanical work (W), and rejects a quantity of heat (Q2) to the sink. According to the First Law of Thermodynamics, for a complete cyclic process, the change in internal energy is zero (Δ U = 0). Therefore, the net work done equals the net heat absorbed:
Thermal Efficiency (η)
The thermal efficiency of a heat engine is defined as the ratio of the net work done by the engine to the total heat energy absorbed from the high-temperature source.
UPSC Prelims Core Takeaway
According to the Kelvin-Planck statement of the Second Law of Thermodynamics, no heat engine can convert all the absorbed heat entirely into work (Q2 cannot be zero). Consequently, the thermal efficiency (η) of a real heat engine is always less than 1 (or less than 100%).
The Carnot Engine: The Ideal Thermodynamic Cycle
Proposed by Nicolas Léonard Sadi Carnot in 1824, the Carnot engine is a theoretical, idealized heat engine that operates on a completely reversible cycle. It establishes the maximum possible efficiency limit for any heat engine operating between two fixed temperatures.
The Four Stages of a Carnot Cycle
The Carnot cycle consists of four sequential reversible processes:
- 1. Isothermal Expansion (at Temperature T1): The working substance is placed in contact with the source. It absorbs heat Q1 and expands isothermally. The temperature remains constant at T1.
- 2. Adiabatic Expansion: The working substance is thermally isolated. It continues to expand and do work, causing its temperature to drop from the source temperature (T1) to the sink temperature (T2).
- 3. Isothermal Compression (at Temperature T2): The working substance is placed in contact with the sink. It is compressed isothermally, rejecting heat Q2 to the sink while maintaining a constant temperature T2.
- 4. Adiabatic Compression: The working substance is thermally isolated and compressed further. The work done on the substance raises its temperature from T2 back to T1, completing the cycle.
Carnot Efficiency Formula
For an ideal Carnot engine, the ratio of heat exchanged is directly proportional to the absolute temperatures of the reservoirs (Q2/Q1 = T2/T1). Thus, the efficiency is written as:
- Note: Temperatures T1 and T2 must always be calculated in Kelvin.
Key Deductions for Carnot Efficiency
- Efficiency depends solely on the temperatures of the source (T1) and sink (T2). It is entirely independent of the nature of the working substance.
- Efficiency increases when the source temperature (T1) is increased or when the sink temperature (T2) is decreased.
- Efficiency can only reach 100% if the sink temperature T2 = 0 K (Absolute Zero), which is practically unattainable according to the Third Law of Thermodynamics.
Classification of Real-World Heat Engines
Real heat engines are broadly categorized into two types based on where the combustion of fuel takes place.
External Combustion Engines (ECE)
The fuel is burned outside the main operating body of the engine to heat a separate working fluid.
- Mechanism: The heat generated by burning fuel (like coal or biomass) boils water in a separate boiler to produce high-pressure steam, which then drives a turbine or piston.
- Examples: Steam locomotives, modern steam turbines used in thermal and nuclear power plants.
Internal Combustion Engines (ICE)
The combustion of fuel occurs directly inside the engine cylinder where the work is performed.
- Mechanism: Fuel reacts chemically with an oxidizer (air) inside a combustion chamber. The high-pressure, high-temperature gases produced expand rapidly, driving pistons or rotors directly.
- Examples: Petrol engines (Otto cycle), Diesel engines (Diesel cycle), gas turbines in jet aircraft.
Comparison of Practical Engine Cycles
| Feature / Metric | Carnot Engine | Petrol Engine (Otto Cycle) | Diesel Engine (Diesel Cycle) |
| Type of Cycle | Theoretical / Ideal | Practical Internal Combustion | Practical Internal Combustion |
| Heat Addition Process | Isothermal (Constant Temperature) | Isochoric (Constant Volume) | Isobaric (Constant Pressure) |
| Heat Rejection Process | Isothermal (Constant Temperature) | Isochoric (Constant Volume) | Isochoric (Constant Volume) |
| Compression Ratio | Variable | Lower (typically 6:1 to 10:1) to prevent knocking. | Higher (typically 15:1 to 22:1) |
| Ignition Mechanism | Non-applicable | Spark Plug initiates ignition. | Compression-ignition (heat of highly compressed air). |
| Practical Efficiency | Maximum possible theoretical limit (∼ 60-70%). | Moderate (∼ 25-30%). | Higher than petrol (∼ 35-42%) due to high compression ratios. |