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

Closed system

-In physics:In thermodynamics, a closed system can exchange energy , but not matter, with its surroundings.In contrast, an isolated system cannot exchange any of heat, work, or matter with the surroundings, while an open system can exchange all of heat, work and matter.For a simple system, with...

 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. .
The process does no pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

-volume work

Work (thermodynamics)

In thermodynamics, work performed by a system is the energy transferred to another system that is measured by the external generalized mechanical constraints on the system. As such, thermodynamic work is a generalization of the concept of mechanical work in mechanics. Thermodynamic work encompasses...

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

For a reversible process

Reversible process (thermodynamics)

In thermodynamics, a reversible process, or reversible cycle if the process is cyclic, is a process that can be "reversed" by means of infinitesimal changes in some property of the system without loss or dissipation of energy. Due to these infinitesimal changes, the system is in thermodynamic...

, the first law of thermodynamics

First law of thermodynamics

The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

 gives the change in the system's internal energy

Internal energy

In thermodynamics, the internal energy is the total energy contained by a thermodynamic system. It is the energy needed to create the system, but excludes the energy to displace the system's surroundings, any energy associated with a move as a whole, or due to external force fields. Internal...

:



Replacing work with a change in volume gives



Since the process is isochoric, , the previous equation now gives



Using the definition of specific heat capacity at constant volume,

,



Integrating both sides yields



Where is the specific heat capacity at constant volume, is initial temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 and is final temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

. We conclude with:


On a pressure volume diagram

Pressure volume diagram

A pressure volume diagram is used to describe corresponding changes in volume and pressure in a system...

, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an isobaric process

Isobaric process

An isobaric process is a thermodynamic process in which the pressure stays constant. The term derives from the Greek isos, , and barus,...

 would appear as a straight horizontal line.

Ideal gas

If an ideal gas

Ideal gas

An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

 is used in an isochoric process, and the quantity of gas

Ideal gas

An ideal gas is a theoretical gas composed of a set of randomly-moving, non-interacting point particles. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics.At normal conditions such as...

 stays constant, then the increase in energy

Energy

In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...

 is proportional to an increase in temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

 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

Otto cycle

An Otto cycle is an idealized thermodynamic cycle which describes the functioning of a typical reciprocating piston engine, the thermodynamic cycle most commonly found in automobile engines....

 is an example of an isochoric process when it is assumed that the burning of the gasoline

Gasoline

Gasoline , or petrol , is a toxic, translucent, petroleum-derived liquid that is primarily used as a fuel in internal combustion engines. It consists mostly of organic compounds obtained by the fractional distillation of petroleum, enhanced with a variety of additives. Some gasolines also contain...

-air mixture in an internal combustion engine

Internal combustion engine

The internal combustion engine is an engine in which the combustion of a fuel occurs with an oxidizer in a combustion chamber. In an internal combustion engine, the expansion of the high-temperature and high -pressure gases produced by combustion apply direct force to some component of the 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."

See also

• Isobaric process
  Isobaric process
  An isobaric process is a thermodynamic process in which the pressure stays constant. The term derives from the Greek isos, , and barus,...
  
  
• Adiabatic process
  Adiabatic process
  In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
  
  
• Cyclic process
• Isothermal process
  Isothermal process
  An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir , and the change occurs slowly enough to allow the system to continually adjust to the temperature of the reservoir...
  
  
• Polytropic process

External links

• http://lorien.ncl.ac.uk/ming/webnotes/Therm1/revers/isocho.htm