Thermodynamic processes and cycles are the backbone of energy conversion systems. They help us understand how heat and work interact in engines, power plants, and refrigerators. This knowledge is crucial for designing efficient machines and tackling energy challenges.

Revisiting these concepts from Thermodynamics I is essential for grasping more advanced topics. We'll explore how different processes combine to form cycles, calculate work and heat transfer, and analyze efficiency. This foundation will prepare you for deeper dives into real-world applications.

Thermodynamic Processes

Isothermal, Isobaric, and Isochoric Processes

• Isothermal processes maintain constant temperature, and the ideal gas law relates changes in pressure and volume
  • Example: Slow compression or expansion of a gas in a piston-cylinder device with heat transfer to maintain constant temperature
• Isobaric processes maintain constant pressure, and the ideal gas law relates changes in temperature and volume
  • Example: Heating a gas in a sealed container with a movable piston, allowing the volume to change while maintaining constant pressure
• Isochoric processes maintain constant volume, and the ideal gas law relates changes in pressure and temperature
  • Example: Heating a gas in a rigid container, causing the pressure to increase while the volume remains constant

Adiabatic Processes and Work Calculations

• Adiabatic processes occur without heat transfer between the system and surroundings, and the relationship between pressure and volume is described by the adiabatic index
  • Example: Rapid compression or expansion of a gas in a piston-cylinder device with insulated walls to prevent heat transfer
• Work done in a process is calculated by integrating pressure with respect to volume, while heat transfer is determined using the first law of thermodynamics
• The direction of heat transfer and work done by or on the system depends on the specific process and can be determined using pressure-volume (P-V) diagrams
• The slope of the process curve on a P-V diagram indicates the type of process: isothermal (hyperbolic), isobaric (horizontal), isochoric (vertical), or adiabatic (steeper than isothermal)
  • Example: A P-V diagram showing an isothermal process as a hyperbolic curve, an isobaric process as a horizontal line, an isochoric process as a vertical line, and an adiabatic process as a curve steeper than the isothermal curve

Work, Heat, and Efficiency

Thermodynamic Cycles and the First Law of Thermodynamics

• Thermodynamic cycles consist of a series of processes that return the system to its initial state, and the net work done by the cycle is the area enclosed by the process curves on a P-V diagram
  • Example: A Carnot cycle represented on a P-V diagram as a rectangle, with the area inside the rectangle representing the net work done by the cycle
• The first law of thermodynamics states that the change in internal energy of a system equals the heat added to the system minus the work done by the system, and this principle is used to calculate heat transfer in a cycle
  • Example: In a Brayton cycle, the heat added in the combustion chamber is equal to the change in internal energy plus the work done by the gas during expansion

Efficiency and the Second Law of Thermodynamics

• Thermal efficiency is the ratio of net work output to heat input in a power cycle, while coefficient of performance (COP) is the ratio of desired heat transfer to work input in a refrigeration or heat pump cycle
  • Example: A Rankine cycle with a net work output of 100 kJ and a heat input of 400 kJ has a thermal efficiency of 25%
• The second law of thermodynamics limits the maximum thermal efficiency of a heat engine operating between two thermal reservoirs, as expressed by the Carnot efficiency formula
  • Example: A heat engine operating between a hot reservoir at 500 K and a cold reservoir at 300 K has a maximum possible (Carnot) efficiency of 40%
• The Carnot cycle, consisting of two isothermal and two adiabatic processes, represents the most efficient possible heat engine or refrigeration cycle operating between two thermal reservoirs
  • Example: A Carnot refrigeration cycle operating between a cold reservoir at 250 K and a hot reservoir at 300 K has a maximum possible COP of 5

Power and Refrigeration Cycles

Internal Combustion Engine Cycles

• The Otto cycle, used in spark-ignition internal combustion engines, consists of isentropic compression, constant-volume heat addition, isentropic expansion, and constant-volume heat rejection
  • Example: A gasoline engine operating on the Otto cycle, with the fuel-air mixture ignited by a spark plug at the end of the compression stroke
• The Diesel cycle, used in compression-ignition internal combustion engines, consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-volume heat rejection
  • Example: A diesel engine operating on the Diesel cycle, with the fuel injected and ignited by the high temperature of the compressed air

Gas Turbine and Steam Power Cycles

• The Brayton cycle, used in gas turbines and jet engines, consists of isentropic compression, constant-pressure heat addition, isentropic expansion, and constant-pressure heat rejection
  • Example: A stationary gas turbine used for power generation, with the high-temperature, high-pressure gas expanding through the turbine to produce work
• The Rankine cycle, used in steam power plants, consists of isentropic compression in a pump, constant-pressure heat addition in a boiler, isentropic expansion in a turbine, and constant-pressure heat rejection in a condenser
  • Example: A coal-fired steam power plant operating on the Rankine cycle, with the steam produced in the boiler expanding through the turbine to generate electricity

Refrigeration and Heat Pump Cycles

• The vapor-compression refrigeration cycle, used in refrigerators and air conditioners, consists of isentropic compression, constant-pressure heat rejection, throttling, and constant-pressure heat absorption
  • Example: A household refrigerator operating on the vapor-compression cycle, with the refrigerant absorbing heat from the cold interior and rejecting heat to the warm room
• Absorption refrigeration cycles, such as the ammonia-water cycle, use a heat source to drive the refrigeration process, with the working fluid absorbing and rejecting heat at different pressures
  • Example: A gas-fired absorption chiller used for air conditioning, with the ammonia-water solution absorbing heat from the conditioned space and rejecting heat to the outdoor environment

Ideal vs Real Cycles

Ideal Cycle Assumptions and Real Cycle Irreversibilities

• Ideal cycles assume reversible processes and perfect components, while real cycles involve irreversibilities such as friction, heat loss, and pressure drops, which reduce efficiency and COP
  • Example: An ideal Rankine cycle assumes isentropic expansion in the turbine, while a real steam turbine experiences entropy generation due to friction and heat loss
• The efficiency of real cycles can be improved by minimizing irreversibilities, such as using heat exchangers, regenerators, or multiple stages of compression and expansion
  • Example: A regenerative Brayton cycle uses a heat exchanger to transfer heat from the turbine exhaust to the compressor outlet, increasing the cycle efficiency

Factors Affecting Cycle Performance

• The efficiency of the Otto cycle is affected by the compression ratio, with higher compression ratios leading to higher efficiencies but also increased risk of engine knocking
  • Example: Increasing the compression ratio of a gasoline engine from 8:1 to 12:1 improves efficiency but may cause knocking if low-octane fuel is used
• The efficiency of the Diesel cycle is affected by the cutoff ratio, which determines the duration of constant-pressure heat addition, with higher cutoff ratios leading to lower efficiencies but reduced peak temperatures and pressures
  • Example: A diesel engine with a higher cutoff ratio (longer fuel injection duration) has a lower efficiency but reduced NOx emissions due to lower peak temperatures
• The efficiency of the Brayton cycle can be improved by increasing the pressure ratio, using regeneration to preheat the incoming air, or employing intercooling and reheating stages
  • Example: A two-stage gas turbine with intercooling and reheating achieves higher efficiency than a simple cycle by reducing compressor work and increasing turbine work
• The efficiency of the Rankine cycle can be improved by increasing the boiler pressure and temperature, using superheat to avoid moisture formation during expansion, or employing regenerative feedwater heating
  • Example: A supercritical steam power plant operates at pressures above the critical point of water, enabling higher efficiencies due to increased boiler temperature
• The COP of vapor-compression refrigeration cycles can be improved by using a compressor with a higher isentropic efficiency, minimizing pressure drops in the condenser and evaporator, or employing multistage compression with intercooling
  • Example: A two-stage refrigeration system with intercooling reduces the compressor work input and increases the COP compared to a single-stage system