A thermodynamic cycle is a series of processes in which a system returns to its initial state after changes in temperature, pressure, and volume. It explains how heat engines convert heat into work and how refrigerators operate. Without this cycle, engines would not run continuously, and cooling systems would not function properly.
There are various types of cycles in thermodynamics, and some of those important cycles are listed as follows:
1. Carnot Cycle
The Carnot cycle was proposed by the French physicist Sadi Carnot in 1824. It is an ideal thermodynamic cycle that represents the maximum possible efficiency of a heat engine. It shows how heat can be reversibly converted into work.
The Carnot cycle consists of four reversible processes:
- Isothermal Expansion: The gas absorbs heat from a hot reservoir and expands at a constant temperature.
- Adiabatic Expansion: The gas expands without heat exchange, doing work and decreasing in temperature.
- Isothermal Compression: The gas releases heat to a cold reservoir at a constant temperature.
- Adiabatic Compression: The gas is compressed without heat exchange, increasing its temperature back to the initial state.
It is important because it sets the maximum efficiency limit for all real heat engines and is used as a standard for comparison.
\eta = 1 - \frac{T_C}{T_H} Where,
- TC is the temperature of the cool supply, and
- TH is the temperature of the hot repository.
The Carnot cycle is an ideal theoretical cycle with maximum efficiency that no real engine can achieve. It is used as a standard to compare the efficiency of heat engines and to determine the maximum performance of refrigerators. It consists of four processes (1-2, 2-3, 3-4, 4-1) showing heat flow and work. It also sets the upper limit of efficiency in thermodynamics.
2. Rankine Cycle
The Rankine cycle is a thermodynamic cycle that explains how steam turbines convert heat energy into mechanical work. It is named after Scottish engineer William John Macquorn Rankine.
It consists of four main steps:
- Isentropic Compression: Water is compressed to high pressure using a pump without heat exchange.
- Heat Addition: High-pressure water is heated in a boiler and converted into steam using fuel sources like coal or gas.
- Isentropic Expansion: Steam expands in a turbine and produces mechanical work.
- Condensation: Steam is cooled in a condenser and converted back into water by releasing heat to the surroundings.
The fundamental thermodynamic cycle used in all steam power plants is the Rankine cycle. Other applications, such as solar thermal power plants and geothermal power plants, also make use of it.
The Rankine cycle is an ideal reversible cycle where heat can be converted into work, but in real systems, losses like friction and heat transfer reduce efficiency to about 30–40%. To improve performance, modified versions such as supercritical, reheat, and regenerative cycles are used, which reduce heat rejection and increase efficiency.
3. Otto Cycle
The Otto cycle is a thermodynamic cycle that explains the working of a spark ignition (petrol) engine. It is named after Nikolaus August Otto, who developed the first four-stroke internal combustion engine in 1876.
It consists of four processes:
- Isentropic Compression: The air-fuel mixture is compressed in the cylinder without heat exchange.
- Constant Volume Heat Addition: The mixture is ignited by a spark, causing combustion at constant volume.
- Isentropic Expansion: Hot gases expand and push the piston down, producing work.
- Constant Volume Heat Rejection: Exhaust gases are released at a constant volume.
The Otto cycle is an ideal model, and real engines do not follow it exactly, but it is widely used to understand petrol engine performance.
The efficiency of the Otto cycle depends on the compression ratio, which is the ratio of the cylinder’s volume at the end of the intake stroke to its volume at the end of the compression stroke. A higher compression ratio results in greater efficiency of the cycle.
4. Diesel Cycle
The Diesel cycle is a thermodynamic cycle that explains the working of a diesel engine. It operates on a four-stroke process and is used in heavy vehicles like trucks and buses.
It consists of four strokes:
- Intake Stroke: Only air is drawn into the cylinder as the piston moves down.
- Compression Stroke: The air is highly compressed, increasing its temperature and pressure.
- Combustion (Power) Stroke: Fuel is injected and ignites due to hot compressed air, pushing the piston downward and producing work.
- Exhaust Stroke: Burnt gases are removed from the cylinder.
The Diesel cycle is more efficient than the Otto cycle due to its higher compression ratio and self-ignition process (no spark plug is used), making it more reliable for heavy-duty applications.
5. Brayton Cycle
The Brayton cycle is a thermodynamic cycle that describes the working of gas turbine engines and jet engines. It uses air or another gas as the working fluid and is widely used in modern power generation and aviation systems.
It consists of four main processes:
- Isentropic Compression: Air is compressed in a compressor without heat exchange, increasing its pressure and temperature.
- Constant Pressure Heat Addition: Fuel is burned at constant pressure, and heat is added to the air, further increasing its temperature.
- Isentropic Expansion: The high-temperature gas expands in a turbine, producing mechanical work.
- Constant Pressure Heat Rejection: Heat is released from the gas at constant pressure to the surroundings using a heat exchanger.
The Brayton cycle is highly efficient for gas turbine systems, but its efficiency is limited by the maximum temperature that materials can withstand in the engine. In practice, compressor and turbine processes are not perfectly isentropic due to losses like friction.
It is commonly used in jet engines, gas turbines, turbochargers, air compressors, and spacecraft power systems.
6. Stirling Cycle
The Stirling cycle is a thermodynamic cycle that explains the working of a Stirling engine, invented by Robert Stirling in 1816. It is a closed-cycle heat engine known for high efficiency and the ability to work with any external heat source, such as solar energy, gas, or waste heat. It is used in power generation, heating, and cooling applications.
The cycle consists of four main processes:
- Isothermal Compression: The working gas is compressed at constant temperature, and heat is released to the surroundings.
- Heat Addition (Regeneration): The gas passes through a regenerator where heat is stored and reused, increasing its temperature and pressure.
- Isothermal Expansion: The heated gas expands at a constant temperature and produces useful work.
- Heat Rejection: The gas releases heat at constant volume to a cold reservoir, decreasing its temperature and pressure.
The Stirling cycle is a closed-loop system, meaning the working fluid remains inside the engine and continuously repeats the cycle.
Solved Problems
Question 1: A Carnot engine operates between a hot reservoir at 600 K and a cold reservoir at 300 K. Find the efficiency of the engine.
Solution:
\eta = 1 - \frac{T_C}{T_H}
\eta = 1 - \frac{300}{600}
\eta = 0.5
\text{Efficiency} = 50\%
Question 2: A heat engine absorbs 1200 J of heat from the hot reservoir and rejects 700 J to the cold reservoir. Find the work done.
Solution:
W = Q_H - Q_C
W = 1200 - 700
W = 500\,J
\text{Work done} = 500\,J
Question 3: A heat engine takes 1500 J of heat from the source and produces 450 J of work. Find the efficiency.
Solution:
\eta = \frac{W}{Q_H}
\eta = \frac{450}{1500}
\eta = 0.3
\text{Efficiency} = 30\%
Question 4: A heat engine has an efficiency of 40% and absorbs 2000 J of heat from the hot reservoir. Find the heat rejected.
Solution:
\eta = \frac{W}{Q_H}
0.4 = \frac{W}{2000}
W = 800\,J
Q_C = Q_H - W
Q_C = 2000 - 800
Q_C = 1200\,J
\text{Heat rejected} = 1200\,J
Unsolved Problems
Question 1: A Carnot engine operates between temperatures of 800 K and 400 K. Find the efficiency of the engine.
Question 2: A heat engine absorbs 2500 J of heat from a hot reservoir and rejects 1500 J to the cold reservoir. Calculate the work done by the engine.
Question 3: A heat engine produces 600 J of work while absorbing 2000 J of heat from the source. Find the efficiency of the engine.
Question 4: A Carnot engine has an efficiency of 35%. If the temperature of the hot reservoir is 700 K, find the temperature of the cold reservoir.
Question 5: A heat engine absorbs 3000 J of heat and performs 900 J of work. Determine the heat rejected to the cold reservoir.