Heat engines are the workhorses of thermodynamics, turning heat into useful work. They're everywhere, from your car's engine to power plants. Understanding how they work is key to grasping the Second Law of Thermodynamics.

Thermal efficiency is the measure of a heat engine's performance. It's all about how much work we can squeeze out of the heat we put in. The Second Law sets limits on this efficiency, showing us why we can't convert all heat into work.

Heat Engines and Components

Definition and Operation

• A heat engine is a thermodynamic system that converts thermal energy from a high-temperature source into mechanical work by exploiting the temperature difference between a hot and cold reservoir
• Heat engines operate cyclically, with the working substance undergoing a series of thermodynamic processes (compression, heating, expansion, and cooling) to transfer heat from the hot reservoir to the cold reservoir while producing net work

Primary Components

• The primary components of a heat engine include:
  • A hot reservoir (heat source)
  • A cold reservoir (heat sink)
  • A working substance (steam or gas)
  • A mechanism to convert the working substance's energy into mechanical work (turbine or piston)

Examples

• Internal combustion engines (gasoline or diesel engines)
• External combustion engines (steam engines or Stirling engines)
• Gas turbines

Thermal Efficiency of Heat Engines

Definition and Formula

• Thermal efficiency is a measure of a heat engine's performance, defined as the ratio of the useful work output ($W$) to the heat input from the hot reservoir ($Q_H$)
• The formula for thermal efficiency is: $\eta = W / Q_H$, where $\eta$ is the thermal efficiency (a dimensionless quantity)

Calculation Using Heat Input and Output

• According to the first law of thermodynamics, the net work output ($W$) is equal to the difference between the heat input from the hot reservoir ($Q_H$) and the heat rejected to the cold reservoir ($Q_C$): $W = Q_H - Q_C$
• Substituting the first law expression into the efficiency formula yields: $\eta = (Q_H - Q_C) / Q_H = 1 - (Q_C / Q_H)$, showing that thermal efficiency can also be calculated using the heat input and heat rejection values

Limitations on Efficiency

• Thermal efficiency is always less than 1 (or 100%) because some heat is inevitably rejected to the cold reservoir, as dictated by the second law of thermodynamics

Factors Influencing Efficiency

Temperature Difference and Working Substance

• The temperature difference between the hot and cold reservoirs is a primary factor affecting thermal efficiency
  • A larger temperature difference generally leads to higher efficiency, as more heat can be converted into work
• The properties of the working substance, such as its specific heat capacity and compressibility, can impact the engine's efficiency by affecting the amount of heat that can be absorbed and the work that can be extracted during the thermodynamic cycle

Irreversibilities and Design

• Friction and other irreversibilities within the engine (heat loss, fluid leakage, or incomplete combustion) reduce the actual thermal efficiency compared to the ideal, reversible case
• The design and configuration of the engine components, such as the compression ratio, valve timing, or turbine blade geometry, can influence efficiency by optimizing the thermodynamic processes and minimizing losses

Operating Conditions

• Operating conditions, including the speed, load, and ambient temperature, can affect efficiency by altering the heat transfer rates, fluid properties, and mechanical losses within the engine

Types of Heat Engines: Comparison

Internal Combustion Engines (ICEs)

• Internal combustion engines burn fuel directly within the engine cylinder, using the heat to drive a piston
  • They are compact and widely used in transportation but have lower thermal efficiencies than some other heat engines
• Gasoline engines use a spark to ignite the fuel-air mixture and typically operate on the Otto cycle (isentropic compression, isochoric heat addition, isentropic expansion, and isochoric heat rejection)
• Diesel engines use compression to ignite the fuel and operate on the Diesel cycle (isentropic compression, isobaric heat addition, isentropic expansion, and isochoric heat rejection)

External Combustion Engines (ECEs)

• External combustion engines burn fuel outside the engine to heat a separate working fluid, such as steam or air
  • They can use various fuels and have potentially higher efficiencies but are generally larger and slower to respond than ICEs
• Steam engines heat water to produce high-pressure steam, which drives a piston or turbine
  • They can operate on the Rankine cycle (isentropic compression in the pump, isobaric heat addition in the boiler, isentropic expansion in the turbine, and isobaric heat rejection in the condenser)
• Stirling engines use a sealed working gas, typically air or helium, which is alternately heated and cooled to drive a piston
  • They operate on the Stirling cycle (isothermal compression, isochoric heat addition, isothermal expansion, and isochoric heat rejection)

Gas Turbines

• Gas turbines compress air, mix it with fuel, and ignite the mixture to produce hot gases that drive a turbine
  • They are used in aircraft propulsion and power generation, offering high power-to-weight ratios and efficiency at optimal operating conditions
• Gas turbines often utilize the Brayton cycle (isentropic compression in the compressor, isobaric heat addition in the combustion chamber, isentropic expansion in the turbine, and isobaric heat rejection in the exhaust)