Heat Engines: Thermodynamics and Cycles

Introduction to Heat Engines

• A heat engine converts thermal energy into mechanical work.
• Heat engines operate by transferring heat from a high-temperature source to a low-temperature sink.
• The rate of heat flow depends on the nature of the contact and the thermal conductivity of the materials.
• Examples of heat engines include steam engines, internal combustion engines, and gas turbines.

Working Principle of Heat Engines

• According to the 2nd Law of Thermodynamics, heat cannot spontaneously flow from a colder body to a hotter body.
• Heat engines perform work by exploiting temperature differences.
• Efficiency is always less than 100% due to inevitable energy losses.

Thermodynamic Cycles

• Heat engines operate on cyclic processes.
• There are four essential thermodynamic processes:
  • Isothermal (constant temperature)
  • Adiabatic (no heat exchange)
  • Isobaric (constant pressure)
  • Isochoric (constant volume)
• Common heat engine cycles include Carnot, Otto, Diesel, Brayton, and Rankine cycles.

The Carnot Cycle

• An ideal heat engine cycle involves four reversible thermodynamic processes between two temperature limits.
• It forms the basis of the 2nd law of thermodynamics and provides a theoretical model for maximum possible efficiency.
• It consists of four operations:
  • Isothermal Expansion (heat absorbed, work done)
  • Adiabatic Expansion (no heat exchange, work done)
  • Isothermal Compression (heat rejected)
  • Adiabatic Compression (no heat exchange)

Carnot Cycle: Isothermal Expansion

• The gas expands, maintaining a constant temperature.
• Heat is absorbed to maintain the constant Temperature.
• The gas performs work on its surroundings, for example, pushing a piston outward.

Carnot Cycle: Adiabatic Expansion

• The gas expands without exchanging heat with the surroundings.
• The system is insulated, preventing heat from entering or leaving.
• The gas does work, decreasing its internal energy and temperature.

Carnot Cycle: Isothermal Compression

• The gas is compressed, maintaining a constant temperature.
• Heat is released to a low-temperature reservoir.
• Work is done on the gas, for instance, pushing a piston inward.

Carnot Cycle: Adiabatic Compression

• The gas is compressed without exchanging heat with the surroundings, as the system is insulated.
• Work is done on the gas, increasing its internal energy and temperature.

Carnot Cycle: Efficiency

• Carnot Efficiency (η) = (T_h - T_c) / T_h = 1 - (T_c / T_h), where T_h and T_c are the absolute temperatures of the hot and cold reservoirs, respectively.

Key Facts on Heat Engines

• It is impossible to take heat from a hotter reservoir and convert it completely into work without transferring part of the heat to a cooler reservoir, implying heat engines can never be 100% efficient.
• It is impossible for a cyclic process to transfer heat from a lower to a higher temperature body without converting some work to heat, recognizing that heat flows spontaneously from hot to cold objects.

Real Heat Engines vs Carnot Engine

• Real engines deviate from the Carnot cycle, due to frictional losses, heat dissipation, and non-ideal gas behavior.
• Carnot efficiency sets the upper limit for real engines.

The Rankine Cycle

• This cycle is commonly used in steam power plants, has a higher efficiency than the Otto cycle, and involves:
  • Isentropic Pumping
  • Isobaric Heat Addition (Boiler)
  • Isentropic Expansion (Turbine Work Output)
  • Isobaric Heat Rejection (Condenser)
• Boiler (or Steam Generator): Heats the working fluid (usually water) to produce high-pressure steam; Process 2-3: Isobaric heat addition occurs here
• Turbine: Converts the thermal energy of the high-pressure steam into mechanical work; Process 3-4: Isentropic expansion occurs here
• Condenser: Condenses the steam back into liquid by rejecting heat to the surroundings; Process 4-1: Isobaric heat rejection occurs here
• Pump: Compresses the liquid working fluid and sends it back to the boiler; Process 1-2: Isentropic compression occurs here

The Otto Cycle

• The Otto cycle describes spark-ignition internal combustion engines (i.e., gasoline engines).
• Gasoline is burned inside the cylinder as opposed to the sterling engine; the working substance is a mixture of air and vaporized gasoline.
• It consists of:
  • Adiabatic Compression (Isentropic Compression)
  • Isochoric Heat Addition (Constant Volume Heat Addition)
  • Adiabatic Expansion (Isentropic Expansion)
  • Isochoric Heat Rejection (Constant Volume Heat Rejection)

The Diesel Cycle

• Found in diesel engines.
• Diesel engines have higher efficiency than the Otto cycle.
• It consists of:
• Adiabatic Compression
• Isobaric Exhaustion
• Adiabatic Expansion
• Isobaric Intake

The Brayton Cycle

• Found in gas turbines and jet engines
• Brayton engines have higher efficiency than the Otto cycle
• It consists of:
• Isentropic Compression
• Isobaric Heat Addition
• Isentropic Expansion
• Isobaric Heat Rejection