Cyclic Processes

Stages of the Cyclic Process

A cyclic process is a series of transformations that takes a gas back to the original state.
Consider the following graph, which shows the processes undergone by an ideal gas:

In the A stage, the gas undergoes a isobaric process.
- Temperature and volume increase in this stage.
- Heat was added in this stage, leading to the increase in temperature and volume, as pressure was kept constant.
In the B stage, an isovolumetric process occurs.
- Pressure and temperature decrease in this stage.
- The gas lost heat in this stage, leading to a decrease in temperature and pressure, as volume was kept constant.
In stage C, the gas undergoes an isobaric process.
- Volume and temperature decrease in this stage.
- The gas lost heat in this stage, leading to a decrease in temperature and volume, as pressure was kept constant.
In the D stage, an isovolumetric process occurs
- Pressure and temperature increase in this stage.
- Heat was added in this stage, leading to the increase in temperature and pressure, as volume was kept constant.
The total change in internal energy throughout the process is 0.
The work done is equal to the area enclosed by the cycle.

Cyclic gas processes are used to run heat engine.
A heat engine is a device that will take energy from a hot body, and use it to do work.

In the above example, heat energy is transferred to the engine from the reactor, and the engine does work on the turbine to spin it.
A heat engine can respond to different cycles and is characterized by its efficiency.
It can be modelled using the following diagram:

The heat engine works in a cycle of 3 steps:
- Heat is extracted from the hot reservoir.
  - For example, heat produced by burning natural gas or from a nuclear reactor.
- Some of the extracted heat is used to provide useful work done.
  - For example, turning a turbine or pushing a piston.
- The unused heat is sent to a cold reservoir.
  - Such as the surroundings.
- The cycle is then repeated.
This model of a heat engine operates under some assumptions, such as the following:
- The heat reservoir is assumed to have an infinite heat capacity, meaning that any heat can be extracted without affecting its temperature.
- The cold reservoir is also assumed to have an infinite heat capacity, allowing any amount of heat to be added without altering its temperature

From a previous diagram we can see that:
- Energy from hot reservoir = work done + energy given to the cold reservoir.
- Using this, and the formula for efficiency, we can calculate the efficiency of a heat engine.

Unfortunately, most heat engines are only around 20% efficient.
A traditional heat engine heats up a gas so that it increases in volume, pushing a piston, which does work.
Once the piston is pushed, the gas is cooled to compress it, bringing the piston back down.
- However, this is very inefficient as it requires constant reheating and cooling.

A more efficient way to get the heat engine to do work would be to supply heat energy at the same temperature as the gas.
The most efficient cycle possible is called a Carnot Cycle, which consists of the following steps:
Isothermal Expansion
- Gas at temperature T1 is in a cylinder and contacting a piston and a heat reservoir.
- The gas is allowed to expand, and as it expands the gas does work on its surroundings, reducing its temperature.
  - However, the heat reservoir, which is the same temperature as the gas, T1, heats it up so that the temperature of the gas stays constant.
  - Thermal energy is transferred to the gas to maintain an isothermal process.

Adiabatic Expansion
- In the second step, the heat reservoir is removed and replaced with insulation.
  - As there is now no heat transfer, the gas undergoes an adiabatic process.
  - As the gas expands now, the temperature reduces to T2.

Isothermal Compression
- In the third step, the insulation is removed, and the gas is exposed to a cold reservoir with temperature T2.
- An external force then pushes on the piston, which would cause an increase in the temperature of the gas.
  - However, increased temperature is transferred to the sink, meaning that both the gas and the sink stay at temperature T2.
  - The cold sink allows this process to be isothermal as thermal energy is transferred to it.

Adiabatic Compression
- In the last step, insulation is added back and the cold sink is removed.
- As the gas continues to be compressed, it returns to its original temperature, T1.
  - In this step, there is an increase in temperature, but no thermal transfer, which shows that this an adiabatic process.

Where TL is the temperature of the cold reservoir and TH is the temperature of the hot reservoir.
This equation shows that the efficiency of Carnot engines is only based on absolute temperature.
Carnot engines have the highest possible efficiency, which means a normal heat engine will always be more inefficient.

Sources

https://allen.in/jee/physics/heat-engine