# Thermodynamic process

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A thermodynamic process is the energetic development of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant. A state function is a thermodynamic variable which depends only on the current state of the system, not the path taken to reach that state. Conversely a process function does depend on the path.

## Overview

An example of a series of thermodynamic processes which make up the Stirling cycle

A thermodynamic process can be visualized by graphically plotting the changes to the system's state variables. In the example, four processes are shown. Each process has a well-defined start and end point in the pressure-volume state space. In this particular example, processes 1 and 3 are isothermal, whereas processes 2 and 4 are isochoric. The PV diagram is a particularly useful visualization of a process, because the area under the curve of a process is the amount of work done by the system during that process. Thus work is considered to be a process variable, as its exact value depends on the particular path taken between the start and end points of the process. Similarly, heat may be transferred during a process, and it too is a process variable. In contrast, pressure and volume (as well as numerous other properties) are considered state variables because their values depend only on the position of the start and end points, not the particular path between them.

## Conjugate variable processes

It is often useful to group processes into pairs, in which each variable held constant is one member of a conjugate pair.

### Pressure - volume

The pressure-volume conjugate pair is concerned with the transfer of mechanical or dynamic energy as the result of work.

• An isobaric process occurs at constant pressure. An example would be to have a movable piston in a cylinder, so that the pressure inside the cylinder is always at atmospheric pressure, although it is isolated from the atmosphere. In other words, the system is dynamically connected, by a movable boundary, to a constant-pressure reservoir.
• An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero. It follows that, for the simple system of two dimensions, any heat energy transferred to the system externally will be absorbed as internal energy. An isochoric process is also known as an isometric process or an isovolumetric process. An example would be to place a closed tin can containing only air into a fire. To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. Mathematically, $\delta Q=dU$. We may say that the system is dynamically insulated, by a rigid boundary, from the environment.

### Temperature - entropy

The temperature-entropy conjugate pair is concerned with the transfer of thermal energy as the result of heating.

• An isothermal process occurs at a constant temperature. An example would be to have a system immersed in a large constant-temperature bath. Any work energy performed by the system will be lost to the bath, but its temperature will remain constant. In other words, the system is thermally connected, by a thermally conductive boundary to a constant-temperature reservoir.
• An adiabatic process is a process in which there is no energy added or subtracted from the system by heating or cooling. For a reversible process, this is identical to an isentropic process. We may say that the system is thermally insulated from its environment and that its boundary is a thermal insulator. If a system has an entropy which has not yet reached its maximum equilibrium value, the entropy will increase even though the system is thermally insulated. Under certain conditions two states of a system may be considered adiabatically accesisble.
• An isentropic process occurs at a constant entropy. For a reversible process this is identical to an adiabatic process. If a system has an entropy which has not yet reached its maximum equilibrium value, a process of cooling may be required to maintain that value of entropy.

### Chemical potential - particle number

The processes above have all implicitly assumed that the boundaries are also impermeable to particles. We may assume boundaries that are both rigid and thermally insulating, but are permeable to one or more types of particle. Similar considerations then hold for the chemical potentialparticle number conjugate pair, which is concerned with the transfer of energy via this transfer of particles.

• In a constant chemical potential process the system is particle-transfer connected, by a particle-permeable boundary, to a constant-µ reservoir.
• In a constant particle number process there is no energy added or subtracted from the system by particle transfer. We may say that the system is particle-transfer-insulated from its environment by a boundary that is impermeable to particles.

## Thermodynamic potentials

Any of the thermodynamic potentials may be held constant during a process. For example:

## Polytropic processes

A polytropic process is a thermodynamic process that obeys the relation:

$P V^{\,n} = C,$

where P is the pressure, V is volume, n is any real number (the "polytropic index"), and C is a constant. This equation can be used to accurately characterize processes of certain systems, notably the compression or expansion of a gas, but in some cases, liquids and solids.

## Quasistatic process

A quasistatic process is an idealized model of a thermodynamic process that happens infinitely slowly(very very slowly). It is important to note that no real process is quasistatic. In practice, such processes can only be approximated by performing them infinitesimally slowly. A quasistatic process often ensures that the system will go through a sequence of states that are infinitesimally close to equilibrium (so the system remains in quasistatic equilibrium), in which case the process is typically reversible.

## References

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