# Isochoric process

﻿
Isochoric process

An isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. An isochoric process is exemplified by the heating or the cooling of the contents of a sealed, inelastic container: The thermodynamic process is the addition or removal of heat; the isolation of the contents of the container establishes the closed system; and the inability of the container to deform imposes the constant-volume condition.

## Formalism

An isochoric thermodynamic process is characterized by constant volume, i.e. ΔV = 0. The process does no pressure-volume work, since such work is defined by

ΔW = PΔV,

where P is pressure. The sign convention is such that positive work is performed by the system on the environment.

For a reversible process, the first law of thermodynamics gives the change in the system's internal energy:

dU = dQdW

Replacing work with a change in volume gives

dU = dQPdV

Since the process is isochoric, dV = 0, the previous equation now gives

dU = dQ

Using the definition of specific heat capacity at constant volume,

Cv = dU / dT,

dQ = nCvdT

Integrating both sides yields

$Q = n\int_a^b \! C \, dT.$

Where C is the specific heat capacity at constant volume, a is initial temperature and b is final temperature. We conclude with:

$Q = n C_v \Delta T\$

Isochoric Process in the Pressure volume diagram. In this diagram, pressure increases, but volume remains constant.

On a pressure volume diagram, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an isobaric process would appear as a straight horizontal line.

### Ideal gas

If an ideal gas is used in an isochoric process, and the quantity of gas stays constant, then the increase in energy is proportional to an increase in temperature and pressure. Take for example a gas heated in a rigid container: the pressure and temperature of the gas will increase, but the volume will remain the same.

## Ideal Otto cycle

The ideal Otto cycle is an example of an isochoric process when it is assumed that the burning of the gasoline-air mixture in an internal combustion engine car is instantaneous. There is an increase in the temperature and the pressure of the gas inside the cylinder while the volume remains the same.

## Etymology

The noun isochor and the adjective isochoric are derived from the Greek words ἴσος (isos) meaning "equal", and χώρα (chora) meaning "space."

## References

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• isochoric process — izochorinis vyksmas statusas T sritis Standartizacija ir metrologija apibrėžtis Termodinaminės sistemos būsenos kitimas, kai jos tūris pastovus. atitikmenys: angl. isochoric process vok. isochore Zustandsänderung, f; isochorer Prozess, m rus.… …   Penkiakalbis aiškinamasis metrologijos terminų žodynas

• isochoric process — izochorinis procesas statusas T sritis chemija apibrėžtis Sistemos būsenos kitimas, kai jos tūris pastovus. atitikmenys: angl. isochoric process rus. изохорный процесс …   Chemijos terminų aiškinamasis žodynas

• isochoric process — izochorinis vyksmas statusas T sritis fizika atitikmenys: angl. isochoric process vok. isochore Zustandsänderung, f; isochorer Prozeß, m rus. изохорический процесс, m; изохорный процесс, m pranc. processus isochore, m …   Fizikos terminų žodynas

• isochoric process — izochorinis procesas statusas T sritis Energetika apibrėžtis Termodinaminis procesas, vykstantis esant pastoviajam sistemos tūriui. atitikmenys: angl. isochoric process vok. isochorer Prozeß, m rus. изохорический процесс, m pranc. processus… …   Aiškinamasis šiluminės ir branduolinės technikos terminų žodynas

• isochoric process — Смотри изохорный процесс …   Энциклопедический словарь по металлургии

• Isochoric — may refer to:*cell transitive, in geometry *isochoric process, in chemistry …   Wikipedia

• isochoric — adjective a) having the same volume b) (of a thermodynamic process) having a constant volume throughout …   Wiktionary

• Thermodynamic process — A thermodynamic process may be defined as the energetic evolution 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 …   Wikipedia

• Isobaric process — An isobaric process is a thermodynamic process in which the pressure stays constant: Delta p = 0 The term derives from the Greek isos, equal, and barus, heavy. The heat transferred to the system does work but also changes the internal energy of… …   Wikipedia

• Polytropic process — A polytropic process is a thermodynamic process that obeys the relation::P V^n = C,where P is 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… …   Wikipedia