Thermodynamic Cycle

Definition

A thermodynamic cycle is a series of thermodynamic processes taking place in a system, where the system undergoes various changes in state (pressure, volume, and temperature) and eventually returns to its original initial state. In such a cycle, the net change in any state function (like internal energy) is zero because the system ends exactly where it began.

Main Content

1. State Variables and Path Functions

• A thermodynamic cycle is defined by state variables such as Pressure (P), Volume (V), and Temperature (T).
• Because the system returns to its initial state, the change in internal energy ($\Delta U$) over a complete cycle is always zero.

2. Energy Interaction (Work and Heat)

• During a cycle, the system interacts with its surroundings through heat transfer ($Q$) and work done ($W$).
• According to the First Law of Thermodynamics, for a complete cycle, the net heat input is equal to the net work output ($\sum Q = \sum W$).

3. Cycle Visualization (P-V Diagram)

• Cycles are typically represented on a Pressure-Volume (P-V) diagram.
• The area enclosed within the path on a P-V diagram represents the net work done by the system during one complete cycle.

Pressure (P)
  ^
  |   ____(2)
  |  /    \
  | (1)    \
  |  \______(3)
  |
  +--------------> Volume (V)
(P-V Diagram showing a closed cycle)

Working / Process

1. Compression Process

• The working fluid (gas or vapor) is compressed, usually by a mechanical component like a piston or compressor.
• During this phase, work is done on the system, leading to an increase in pressure and temperature of the fluid.

2. Heat Addition Process

• Energy is introduced into the system from an external heat source (e.g., combustion or an external heater).
• This process causes the fluid to expand or increase its internal energy, preparing it to perform work.

3. Expansion and Heat Rejection

• The high-pressure fluid expands against a piston or turbine blade, performing useful work by the system.
• Finally, heat is rejected to a cold reservoir, cooling the fluid and returning it to the initial state to restart the cycle.

Advantages / Applications

• Power Generation: Thermodynamic cycles like the Rankine cycle are the foundation of steam power plants that produce electricity.
• Transportation: Internal combustion engine cycles (Otto and Diesel cycles) power cars, trucks, and airplanes.
• Refrigeration: The Reversed Carnot or Vapor-Compression cycle is used in refrigerators and air conditioning systems to transfer heat from a cold space to a warm environment.

Summary

A thermodynamic cycle is a closed loop of energy transformation where a system returns to its original state, ensuring that the net change in internal energy is zero. These cycles are fundamental to converting heat into mechanical work or transferring heat for cooling purposes.

• Key point: Net internal energy change equals zero.
• Key point: Net heat transferred equals net work performed.
• Key point: P-V diagrams are essential tools for calculating cycle work.
• Important terms: State Variables, P-V Diagram, Heat Reservoir, Working Fluid, Adiabatic Process, Isothermal Process.