Heat engine
A heat engine is a device that extracts heat from a high-temperature source, converts a portion of it into mechanical work, and rejects the remainder to a low-temperature sink, operating through a repeating thermodynamic cycle.[1] These engines are fundamental to converting thermal energy into useful work in applications ranging from automotive internal combustion engines to large-scale power generation systems.[2] The operation of a heat engine relies on the second law of thermodynamics, which states that it is impossible to convert all heat from a reservoir into work without some waste heat being expelled, limiting the efficiency of the process.[3] Key components include a hot reservoir (e.g., combustion chamber or nuclear reactor), a cold reservoir (e.g., atmosphere or cooling water), and a working substance (e.g., gas or steam) that undergoes cyclic changes in pressure, volume, and temperature to produce net work.[1] The efficiency \eta of a heat engine is defined as the ratio of work output W to heat input Q_h, given by \eta = \frac{W}{Q_h} = 1 - \frac{Q_c}{Q_h}, where Q_c is the heat rejected to the cold reservoir; real engines achieve efficiencies typically between 20% and 40%, far below theoretical maxima.[2][3] The theoretical foundation for heat engine efficiency was established by Sadi Carnot in 1824 through his analysis of an idealized reversible cycle, known as the Carnot cycle, which operates via two isothermal and two adiabatic processes and sets the upper limit for efficiency as \eta = 1 - \frac{T_c}{T_h}, where T_h and T_c are the absolute temperatures of the hot and cold reservoirs, respectively.[3] Common types include external combustion engines like steam turbines, which powered the Industrial Revolution, and internal combustion engines such as the Otto cycle in gasoline vehicles or the Diesel cycle in heavy machinery.[1] Despite advances, all heat engines are constrained by entropy production in irreversible processes, underscoring the second law's role in dictating fundamental limits on energy conversion.[3]Introduction
Definition and Scope
A heat engine is a device that converts thermal energy extracted from a hot reservoir into mechanical work, while expelling the remaining unusable energy as waste heat to a cold reservoir.[4] This process typically involves a working fluid, such as a gas or vapor, that undergoes changes in state to facilitate the energy transfer./University_Physics_II_-Thermodynamics_Electricity_and_Magnetism(OpenStax)/04%3A_The_Second_Law_of_Thermodynamics/4.03%3A_Heat_Engines) The scope of heat engines is confined to systems that operate through cyclic thermodynamic processes, where the working fluid returns to its initial state after each cycle, ensuring continuous operation.[4] These processes are fundamentally governed by the second law of thermodynamics, which dictates that not all heat input can be converted to work, as some must be rejected to the cold reservoir to maintain the cycle. Heat engines exclude non-cyclic devices or those that convert energy through non-thermal means, such as electrochemical reactions in fuel cells, which directly transform chemical potential into electrical work without relying on temperature gradients.[5] In contrast to refrigerators and heat pumps, which require net work input to transfer heat from a cold source to a hot sink against the natural flow, heat engines produce a net work output by exploiting the spontaneous flow of heat from hot to cold. This fundamental directional difference underscores their roles: heat engines generate useful mechanical energy, whereas refrigerators and heat pumps achieve cooling or heating effects./University_Physics_II_-Thermodynamics_Electricity_and_Magnetism(OpenStax)/04%3A_The_Second_Law_of_Thermodynamics/4.04%3A_Refrigerators_Heat_Pumps_and_the_First_Law_of_Thermodynamics) Key terminology includes the heat input from the hot reservoir (Q_h), the heat rejected to the cold reservoir (Q_c), and the net work output (W), with thermal efficiency defined as the ratio W/Q_h.[4] These quantities form the basis for analyzing engine performance within thermodynamic constraints.[6]Basic Components and Operation
A heat engine fundamentally comprises four core components: a hot reservoir serving as the source of high-temperature heat, a working fluid—typically a gas, liquid, or phase-changing substance like steam—that undergoes thermodynamic changes, a cold reservoir acting as the sink for rejected waste heat, and a mechanical linkage such as a piston in reciprocating engines or blades in turbines that converts the fluid's energy into useful mechanical work.[7][8][9] The operational sequence of a heat engine follows a cyclic process involving heat absorption, expansion for work extraction, heat rejection, and compression to restore the initial state. The working fluid first absorbs heat Q_h from the hot reservoir, causing it to expand and drive the mechanical linkage to produce work. This is followed by the rejection of lower-grade heat Q_c to the cold reservoir, after which the fluid is compressed, often with minimal work input, to complete the cycle and prepare for renewed heat absorption.[7][8] This sequence adheres to the first law of thermodynamics, which states that the change in internal energy over a complete cycle is zero (\Delta U = 0), implying that the net work output equals the difference between absorbed and rejected heat: W_{net} = Q_h - Q_c.[7] The directional flow of operation—from hot to cold reservoir—is enforced by the second law of thermodynamics, which dictates that heat transfers spontaneously only from higher to lower temperatures and prohibits devices that could convert heat entirely into work without such a differential, thereby ruling out perpetual motion machines of the second kind.[10][11]Thermodynamic Principles
Fundamental Laws and Cycles
The zeroth law of thermodynamics establishes the concept of thermal equilibrium, stating that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.[12] This law provides the foundation for defining temperature as a measurable property of systems in equilibrium, which is essential for heat engines to operate by identifying hot and cold reservoirs.[13] Without this prerequisite, the consistent transfer of heat between components in a heat engine would be impossible to quantify or control. The first law of thermodynamics, a statement of energy conservation, asserts that the change in internal energy of a closed system equals the heat added to the system minus the work done by the system.[14] In the context of heat engines, this law ensures that the work output derives from the conversion of heat input, with no net creation or destruction of energy during the process.[15] It sets the basic framework for heat-to-work conversion but does not address the directionality or efficiency of such transformations. The second law of thermodynamics introduces the principle of directionality in natural processes, with two equivalent statements relevant to heat engines: the Clausius statement, which prohibits heat from spontaneously flowing from a colder body to a hotter one without external work, and the Kelvin-Planck statement, which declares that no heat engine can convert all absorbed heat into work without rejecting some heat to a colder reservoir.[16] These statements imply the existence of entropy, a measure of disorder or unavailable energy, which increases in all irreversible processes, including those in real heat engines due to friction, heat leaks, and finite temperature differences.[17] Consequently, complete conversion of heat to work is impossible, mandating waste heat expulsion and limiting engine performance.[18] A thermodynamic cycle in a heat engine consists of a closed loop of processes that returns the working substance to its initial state, enabling repeated operation without net change in system properties.[19] Cycles are classified as reversible, where the system and surroundings can be restored to their original states with no net entropy change, or irreversible, where entropy increases due to dissipative effects like friction or unrestrained expansion.[20] Reversible cycles serve as theoretical ideals for analyzing maximum possible efficiency, while irreversible cycles reflect practical operations with inherent losses. Among idealized cycles, the Carnot cycle stands as the benchmark for heat engine performance, comprising two reversible isothermal processes—at constant temperature, where heat is absorbed from a hot reservoir and rejected to a cold one—and two reversible adiabatic processes—without heat transfer, involving expansion and compression.[21] Proposed by Sadi Carnot in 1824, this cycle achieves the highest possible efficiency for given reservoir temperatures but remains unattainable in practice because real processes inevitably involve irreversibilities that increase entropy.[22]Key Processes in Heat Engines
Heat engines operate through a series of thermodynamic processes that convert thermal energy into mechanical work, typically idealized in cycles like the Carnot cycle. These processes are reversible in the ideal case, ensuring maximum efficiency, and include two isothermal steps where heat transfer occurs at constant temperature and two adiabatic steps where no heat is exchanged. The working fluid, often modeled as an ideal gas, undergoes changes in pressure, volume, temperature, and entropy during these steps, governed by the first and second laws of thermodynamics.[23][24] The first key process is isothermal heat addition, where the working fluid absorbs heat Q_h from a high-temperature reservoir at constant temperature T_h. During this expansion, the fluid's internal energy remains unchanged for an ideal gas, so the absorbed heat fully converts to work output, with the volume increasing while pressure decreases. This process increases the entropy of the system by \Delta S = Q_h / T_h, as heat transfer occurs reversibly at constant temperature.[23][25] Following this is the adiabatic expansion, an isentropic process where the fluid expands without any heat transfer (Q = 0), converting internal energy into additional work. For an ideal gas, the pressure and volume follow the relation P V^{\gamma} = \constant, where \gamma = C_p / C_v is the heat capacity ratio (e.g., \gamma = 5/3 for monatomic gases). The temperature decreases as the fluid does work, with entropy remaining constant due to the reversibility. This step steepens the pressure-volume curve compared to isothermal expansion.[26][27] The third process, isothermal heat rejection, occurs at a lower constant temperature T_c, where the fluid releases heat Q_c to a cold reservoir while contracting. Similar to heat addition, internal energy is unchanged, and the rejected heat equals the work input, decreasing the system's entropy by \Delta S = -Q_c / T_c. Volume decreases as pressure rises, maintaining thermal equilibrium with the reservoir.[23][25] Finally, adiabatic compression reverses the expansion: the fluid is compressed without heat transfer, requiring work input to increase its internal energy and temperature back toward T_h. Again, for an ideal gas, P V^{\gamma} = \constant holds, with entropy constant and no heat exchange. This process prepares the fluid for the next cycle by restoring initial conditions.[26][27] These processes are visualized using pressure-volume (P-V) and temperature-entropy (T-S) diagrams. In a P-V diagram, isothermal processes appear as hyperbolas (P V = \constant), while adiabatics are steeper curves; the enclosed area represents net work. The T-S diagram shows horizontal lines for isothermals (with entropy changes) and vertical lines for adiabatics (constant entropy), highlighting the cycle's reversibility through equal entropy increases and decreases. In real engines, irreversibilities such as mechanical friction, fluid turbulence, and unintended heat losses across finite temperature differences degrade these ideal processes, reducing efficiency by generating entropy.[24][23][28]Classification and Examples
Conventional Macroscopic Engines
Conventional macroscopic heat engines encompass traditional large-scale devices that convert thermal energy into mechanical work, primarily through external or internal combustion processes, and are widely employed in industrial and transportation sectors. External combustion engines, where heat is supplied from an external source to a working fluid, include steam engines operating on the Rankine cycle and Stirling engines. The Rankine cycle, fundamental to steam power plants, involves four key components: a boiler where water is heated to produce high-pressure steam, a turbine that extracts work from the expanding steam, a condenser that liquefies the exhaust steam, and a pump that returns the liquid water to the boiler.[29] In this cycle, latent heat plays a crucial role during the phase change in the boiler, where water evaporates into steam, absorbing significant energy at constant temperature to enable efficient heat addition and subsequent work extraction in the turbine.[30] The Stirling engine, another external combustion type, operates as a closed-cycle regenerative heat engine using a permanently gaseous working fluid, such as air or helium, where heat is transferred through cyclic compression and expansion with internal regeneration to store and reuse thermal energy, minimizing losses.[31] Internal combustion engines, which burn fuel directly within the working chamber, dominate automotive and heavy-duty applications through cycles like the Otto and Diesel. The Otto cycle models spark-ignition gasoline engines, featuring constant-volume heat addition via spark-induced combustion after isentropic compression, followed by expansion and exhaust, enabling efficient operation in passenger vehicles.[32] In contrast, the Diesel cycle powers compression-ignition engines using diesel fuel, with heat addition occurring at constant pressure during fuel injection and combustion after high compression, which allows for higher compression ratios and better fuel economy in trucks and generators.[33] Gas turbines, operating on the Brayton cycle, provide continuous-flow power through a compressor that pressurizes intake air, a combustor that adds heat at constant pressure by burning fuel, and a turbine that drives both the compressor and an external load, such as a propeller or generator.[34] These engines find broad applications in automotive propulsion via Otto and Diesel cycles, stationary power generation using steam turbines, gas turbines, and reciprocating engines, and marine propulsion primarily through large Diesel engines and gas turbines for ships.[35] Typical thermal efficiencies for internal combustion engines range from 20% to 40%, influenced by factors like compression ratio and load conditions, though real-world performance varies with design and operation.[36]Specialized and Natural Heat Engines
The Earth's atmosphere operates as a planetary heat engine, powered by solar radiation that unevenly heats the surface, driving convection currents, wind patterns, and weather systems through the redistribution of thermal energy.[37] This process converts absorbed solar energy into mechanical work, such as atmospheric circulation, while dissipating excess heat to space via radiation.[38] The overall efficiency of this natural heat engine is approximately 1-2%, limited by irreversible processes like friction in air flows and radiative losses, far below theoretical Carnot limits due to the broad temperature range from surface highs to cosmic background lows.[39] Refrigeration cycles function as specialized reverse heat engines, absorbing heat from a low-temperature reservoir and rejecting it to a higher one, typically using external work or heat input, with performance measured by the coefficient of performance (COP), defined as the ratio of cooling effect to input energy. The vapor-compression cycle, akin to a reversed Rankine cycle, employs four key components: a compressor to raise refrigerant pressure and temperature, a condenser to release heat, an expansion valve to reduce pressure, and an evaporator to absorb heat, achieving COP values of 3-5 in practical systems depending on operating temperatures.[40] In contrast, absorption cycles replace mechanical compression with thermal absorption using an absorbent-refrigerant pair, such as ammonia-water, driven by heat from sources like waste streams, yielding lower COPs around 0.7 for air conditioning applications but enabling operation without electricity.[41] Evaporative heat engines leverage humidity gradients and water evaporation to produce cooling or limited mechanical work, exploiting the latent heat of vaporization to transfer energy without moving parts.[42] In these systems, dry air passes over water-saturated media, where evaporation cools the air stream by absorbing heat, increasing humidity while lowering temperature by up to 15-20°C in arid conditions, though effectiveness diminishes in high-humidity environments.[43] At mesoscopic and nanoscale regimes, heat engines manipulate electron flow or molecular vibrations to harvest thermal energy, operating under quantum and fluctuation-dominated thermodynamics distinct from macroscopic counterparts.[44] These devices, often fabricated in solid-state systems, convert heat gradients into directed electron currents or mechanical oscillations at the single-molecule level, with prototypes demonstrating work extraction from ambient fluctuations via ratchet-like mechanisms.[45] Magnetic cycles, based on the magnetocaloric effect, enable cooling by cyclically applying and removing magnetic fields to materials like gadolinium, causing reversible temperature changes of several kelvins near Curie points, achieving COPs up to 10 in prototype refrigerators for near-room-temperature applications.[46] Phase-change and liquid-only heat engines adapt thermodynamic cycles for low-grade heat sources, prioritizing organic or alternative fluids over steam to avoid phase-change challenges at reduced temperatures. The Organic Rankine Cycle (ORC) uses organic working fluids like refrigerants in a closed loop to generate power from waste heat between 80-200°C, with typical thermal efficiencies of 5-15% depending on fluid selection and temperature differential, enabling recovery from industrial processes or geothermal sources.[47] Thermoelectric engines, grounded in the Seebeck effect where temperature differences across junctions of dissimilar materials induce voltage via charge carrier diffusion, operate without fluids or moving parts, converting heat directly to electricity with efficiencies reaching 10% for materials with figure-of-merit ZT around 1.25, suitable for waste heat scavenging in electronics.[48]Efficiency and Performance
Theoretical Efficiency Limits
The Carnot theorem establishes that no heat engine operating between two thermal reservoirs can exceed the efficiency of a reversible Carnot engine operating between the same reservoirs, and that all reversible engines between those reservoirs achieve identical efficiency.[49] This theorem, originally articulated by Sadi Carnot in his 1824 analysis of ideal heat engines, underscores the second law of thermodynamics by prohibiting any process from converting heat entirely into work without some rejection to a colder reservoir.[50] The maximum efficiency of a reversible heat engine, known as the Carnot efficiency, is derived from the condition of zero net entropy change in a cyclic process. For a reversible cycle, the total entropy change is \Delta S = 0 = \frac{Q_h}{T_h} + \frac{Q_c}{T_c}, where Q_h > 0 is the heat absorbed from the hot reservoir at temperature T_h and Q_c < 0 is the heat rejected to the cold reservoir at T_c (both temperatures in Kelvin). Rearranging gives \frac{|Q_c|}{Q_h} = \frac{T_c}{T_h}. The efficiency \eta is then the ratio of net work output to heat input, \eta = \frac{W}{Q_h} = 1 - \frac{|Q_c|}{Q_h} = 1 - \frac{T_c}{T_h}.[51] This formula holds regardless of the working fluid, as the derivation relies solely on thermodynamic reversibility and the temperatures of the reservoirs. The implications of Carnot efficiency are profound: it sets an absolute upper bound on heat engine performance, dependent only on the temperature ratio, which limits practical applications to scenarios with significant temperature differences. For instance, with T_h = 800 K and T_c = 300 K, \eta_{Carnot} \approx 62.5\%, illustrating that even ideal engines cannot approach 100% efficiency without an infinite temperature ratio.[51] To address limitations of the infinite-time reversible assumption, endo-reversible models within finite-time thermodynamics provide bounds that assume internal reversibility but incorporate external irreversibilities from finite-rate heat transfer. In these models, the engine operates between intermediate temperatures due to thermal gradients at the boundaries, yielding a maximum power efficiency of \eta = 1 - \sqrt{T_c / T_h}, as derived by Curzon and Ahlborn for an endoreversible Carnot engine.[52] This expression offers a more attainable target for real systems prioritizing power output over ultimate efficiency.Real-World Efficiency and Losses
In practical heat engines, efficiency is invariably lower than theoretical limits due to various irreversibilities that generate entropy and dissipate useful energy. These losses stem primarily from friction in moving parts, such as bearings and pistons, which converts mechanical energy into heat; heat transfer across finite temperature differences, leading to irreversible conduction; incomplete combustion in engines where fuel is not fully oxidized, resulting in unburned hydrocarbons and chemical energy loss; and inefficiencies in pumps, turbines, and compressors due to fluid friction and non-ideal flow. Additionally, second law losses arise from entropy generation during processes like mixing of gases, chemical reactions, and throttling, which reduce the available work potential beyond what reversible models predict.[53][54][55] Performance in real-world heat engines is quantified using metrics that account for these losses. The thermal efficiency, defined as η = W_net / Q_in, where W_net is the net work output and Q_in is the heat input, measures the fraction of thermal energy converted to useful work. Specific fuel consumption (SFC), often expressed as brake specific fuel consumption (BSFC) in grams of fuel per kilowatt-hour, indicates fuel usage per unit power and inversely relates to efficiency. Exergy analysis provides a more comprehensive assessment by evaluating the maximum available work from energy streams, highlighting destruction due to irreversibilities like those mentioned above, and is particularly useful for identifying loss hotspots in complex systems such as power plants.[53][56] Typical thermal efficiencies vary by engine type and are constrained by material limits, such as maximum operating temperatures around 1,000–1,500°C for turbine blades to avoid creep and oxidation. Coal-fired steam power plants achieve 30–40% efficiency, limited by boiler and condenser losses. Internal combustion engines range from 20–35% for gasoline variants, affected by pumping and heat rejection, to 30–45% for diesel engines with higher compression ratios. Combined cycle plants, integrating gas and steam turbines, reach up to 60% by recovering exhaust heat, though real values often fall to 50–55% due to component mismatches. These figures underscore the gap to Carnot limits, often 10–20 percentage points lower in practice.[57][58][59]| Engine Type | Typical Thermal Efficiency (%) | Key Limiting Factors |
|---|---|---|
| Coal-Fired Steam Plant | 30–40 | Heat transfer losses, material temperature limits |
| Gasoline IC Engine | 20–35 | Incomplete combustion, friction |
| Diesel IC Engine | 30–45 | Pumping losses, entropy in expansion |
| Combined Cycle Plant | 50–60 | Turbine inefficiencies, heat recovery limits |