In
thermodynamics
Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of the ...
, an isochoric process, also called a constant-volume process, an isovolumetric process, or an isometric process, is a
thermodynamic process
Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes.
(1)A Thermodynamic process is a process in which the thermodynamic state of a system is change ...
during which the
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
of the
closed system
A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed.
In ...
undergoing such a process remains constant. An isochoric process is exemplified by the heating or the cooling of the contents of a sealed,
inelastic
In economics, elasticity measures the percentage change of one economic variable in response to a percentage change in another. If the price elasticity of the demand of something is -2, a 10% increase in price causes the demand quantity to fall ...
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
Deformation can refer to:
* Deformation (engineering), changes in an object's shape or form due to the application of a force or forces.
** Deformation (physics), such changes considered and analyzed as displacements of continuum bodies.
* De ...
imposes the constant-volume condition. The isochoric process here should be a
quasi-static process
In thermodynamics, a quasi-static process (also known as a quasi-equilibrium process; from the Latin ''quasi'', meaning ‘as if’), is a thermodynamic process that happens slowly enough for the system to remain in internal physical (but not nec ...
.
Formalism
An isochoric thermodynamic
quasi-static process is characterized by constant
volume
Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
, i.e., .
The process does no
pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
-volume
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal tr ...
, since such work is defined by
where is pressure. The sign convention is such that positive work is performed by the system on the environment.
If the process is not quasi-static, the work can perhaps be done in a volume constant thermodynamic process.
For a
reversible process, the
first law of thermodynamics
The first law of thermodynamics is a formulation of the law of conservation of energy, adapted for thermodynamic processes. It distinguishes in principle two forms of energy transfer, heat and thermodynamic work for a system of a constant amoun ...
gives the change in the system's
internal energy
The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
:
Replacing
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal tr ...
with a change in volume gives
Since the process is isochoric, , the previous equation now gives
Using the definition of
specific heat capacity
In thermodynamics, the specific heat capacity (symbol ) of a substance is the heat capacity of a sample of the substance divided by the mass of the sample, also sometimes referred to as massic heat capacity. Informally, it is the amount of heat t ...
at constant volume, , where is the mass of the gas, we get
Integrating both sides yields
where is the specific heat capacity at constant volume, is the initial
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
and is the final
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
. We conclude with:
![isochoric process SVG](https://upload.wikimedia.org/wikipedia/commons/9/9d/Isochoric_process_SVG.svg)
On a
pressure volume diagram
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
, an isochoric process appears as a straight vertical line. Its thermodynamic conjugate, an
isobaric process
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: Δ''P'' = 0. The heat transferred to the system does work, but also changes the internal energy (''U'') of t ...
would appear as a straight horizontal line.
Ideal gas
If an
ideal gas
An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is a ...
is used in an isochoric process, and the quantity of
gas
Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).
A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...
stays constant, then the increase in
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
is proportional to an increase in
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
and pressure. 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
An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.
The Otto cycle is a description of what happ ...
is an example of an isochoric process when it is assumed that the burning of the
gasoline
Gasoline (; ) or petrol (; ) (see ) is a transparent, petroleum-derived flammable liquid that is used primarily as a fuel in most spark-ignited internal combustion engines (also known as petrol engines). It consists mostly of organic co ...
-air mixture in an
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal combus ...
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
Greek may refer to:
Greece
Anything of, from, or related to Greece, a country in Southern Europe:
*Greeks, an ethnic group.
*Greek language, a branch of the Indo-European language family.
**Proto-Greek language, the assumed last common ancestor ...
words ἴσος (''isos'') meaning "equal", and χώρα (''khṓra'') meaning "space."
See also
*
Isobaric process
In thermodynamics, an isobaric process is a type of thermodynamic process in which the pressure of the system stays constant: Δ''P'' = 0. The heat transferred to the system does work, but also changes the internal energy (''U'') of t ...
*
Adiabatic process
In thermodynamics, an adiabatic process (Greek: ''adiábatos'', "impassable") is a type of thermodynamic process that occurs without transferring heat or mass between the thermodynamic system and its environment. Unlike an isothermal process, ...
*
Cyclic process
A thermodynamic cycle consists of a linked sequence 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 eventual ...
*
Isothermal process
In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...
*
Polytropic process
A polytropic process is a thermodynamic process that obeys the relation:
p V^ = C
where ''p'' is the pressure, ''V'' is volume, ''n'' is the polytropic index, and ''C'' is a constant. The polytropic process equation describes expansion and comp ...
References
{{DEFAULTSORT:Isochoric Process
Thermodynamic processes