Thermodynamics And Statistical Mechanics Codexery

Thermodynamic cycle

A cycle returns a system to its initial state.

Thermodynamic cycle

A thermodynamic cycle is a series of linked processes where a system exchanges heat and work with its surroundings, changing properties like pressure and temperature, but ultimately returning to its starting state. This repeating loop allows for continuous operation, making cycles a key idea in thermodynamics. In such a cycle, the working fluid can take heat from a warm source, convert some of it into useful work, and dump the leftover heat into a cold sink—this is a heat engine. Reversing the cycle uses work to move heat from a cold source to a warm sink, acting as a heat pump. If the system stays in thermodynamic equilibrium at every step, the cycle is reversible. Regardless of reversibility, the system’s net entropy change over the full cycle is zero, since entropy is a state function.

During a closed cycle, the system returns to its original temperature and pressure. Quantities like heat and work depend on the path taken. The first law of thermodynamics says that for a complete cycle, the change in internal energy (ΔU) is zero: energy in minus energy out equals zero. So, the total work and heat input equals the total work and heat output. On a pressure-volume (P-V) diagram, the cycle forms a closed loop. The area inside that loop equals the net work done by the cycle, which is also equal to the net heat transferred (heat in minus heat out). If the loop goes clockwise, net work is positive, and the cycle acts as a heat engine. If counterclockwise, net work is negative, and it acts as a heat pump.

Two main types of thermodynamic cycles are power cycles and heat pump cycles. Power cycles turn heat input into mechanical work output, while heat pump cycles use mechanical work to move heat from low to high temperatures. Cycles made of quasistatic processes can operate as either type by simply reversing direction. Common processes used to build cycles include adiabatic (no heat transfer, only work) and isothermal (constant temperature).

field
Thermodynamics
known_for
Power cycles and heat pump cycles; basis for heat engines and heat pumps
key_property
Net entropy change of the system is zero over a complete cycle
first_law_relation
ΔU = 0 over the cycle; net work equals net heat transfer

Lore & Background

A thermodynamic cycle consists of linked sequences of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. In the process of passing through a cycle, the working fluid may convert heat from a warm source into useful work, and dispose of the remaining heat to a cold sink, thereby acting as a heat engine. Conversely, the cycle may be reversed and use work to move heat from a cold source and transfer it to a warm sink thereby acting as a heat pump.

Reader's Guide

Thermodynamic cycles are fundamental to the operation of heat engines, which supply most of the world's electric power and run the vast majority of motor vehicles. Power cycles convert some heat input into a mechanical work output, while heat pump cycles transfer heat from low to high temperatures by using mechanical work as the input. On a pressure–volume (PV) diagram or temperature–entropy diagram, the clockwise and counterclockwise directions indicate power and heat pump cycles, respectively. The area enclosed by the loop on a P-V diagram is the net work done by the cycle, equal to the net heat transferred. Common processes used in cycles include adiabatic, isothermal, isobaric, isochoric, isentropic, isenthalpic, polytropic, and reversible processes. The Otto cycle is an example of a reversible thermodynamic cycle, consisting of isentropic expansion, isochoric cooling, isentropic compression, and isochoric heating.

Did You Know?

Frequently Asked Questions

What exactly is a thermodynamic cycle?

It is a closed loop of linked thermodynamic processes in which heat and work flow into and out of a system, shifting pressure, temperature, and other state variables along the way, before the system snaps back to its exact starting state. Because the path can repeat indefinitely, it underpins continuous operation in engines, refrigerators, and heat pumps.

Why is the net entropy change of the system zero over a complete cycle?

Entropy is a state function, so when the system returns to its initial state every state variable—including entropy—must be identical to where it started. Any entropy carried in during one segment of the path is exactly offset by entropy carried out in another, leaving the system with no net change.

What does the first law of thermodynamics demand for a full cycle?

Since internal energy is a state function, ΔU over the entire cycle is zero, which forces the net work delivered by the system to equal the net heat transferred into it. That single accounting identity is the backbone of every power-cycle and heat-pump design.

What are the two main families of thermodynamic cycles that fans and engineers talk about?

Power cycles (Carnot, Otto, Diesel, Brayton, etc.) convert absorbed heat into useful net work, while heat-pump cycles (vapor-compression, absorption) use work input to shuttle heat from a cold reservoir to a hot one. They are essentially mirror images of the same underlying cycle logic.

Why do textbooks and fan wikis model cycles as quasistatic processes?

Quasistatic idealization lets you trace a smooth, reversible path on a P-V or T-S diagram and evaluate exact work and heat integrals. Real machines deviate through friction and irreversibility, but the quasistatic benchmark gives the upper-bound performance every actual cycle is judged against.

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