Isochoric process

In thermodynamics, 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. The isochoric process here should be a quasi-static process.


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

If the process is not quasi-static, the work can perhaps be done in a volume constant thermodynamic process.[1]

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


Replacing work with a change in volume gives


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


Using the definition of specific heat capacity at constant volume, cv = (dQ/dT)/m, where m is the mass of the gas, we get


Integrating both sides yields


Where cv is the specific heat capacity at constant volume, T1 is the initial temperature and T2 is the final temperature. We conclude with:

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 gasEdit

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. 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 cycleEdit

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.


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


Isochoric freezing has been proposed as a food processing technology. It is claimed to reduce energy use while preserving the quality of the food better than traditional methods.[2]

The concept of Isochoric processes are currently being explored for a variety of applications. Specifically, Isochoric Supercooling has found an interesting and novel application in the field of tissue preservation. Recent research from Dr. Powell-Palm group focuses on focuses on using the Isochoric Supercooling technique as a low cost alternative to store complex biologics which generally have a very short ex-vivo life and are usually stored for a day or two using expensive cryopreservation methods. Isochoric supercooling shows promising results, with being able to store tissues for multiple days without the necessity to use any kind of expensive cryoprotectants such as dimethyl sulfoxide (DMSO) or glycerol. As shown by the group, this method of preservation using isochoric supercooling does not cause any damage to the structural integrity of the tissue nor their responsiveness to drug exposure following revival. [3]

While the demand for transplant organs keep increasing day by day, with over 100,000 people on transplant waiting lists in just the U.S. alone, more than 70% of all thoracic donor organs are discarded each year, due to not being able to preserve them for sufficient time periods.[4] In such a scenario, the Isochoric supercooling may prove to be a better alternative for preserving tissues in a cheaper and simple manner.

See alsoEdit


  1. ^ "If gas volume remains constant, it can do work?". Retrieved 17 April 2018.
  2. ^ Puiu, Tibi (2021-09-10). "A radical new freezing method could cut emissions equal to one million cars, while keeping your food fresh". ZME Science. Retrieved 2021-09-11.
  3. ^ Powell-Palm, Matthew J.; Charwat, Verena; Charrez, Berenice; Siemons, Brian; Healy, Kevin E.; Rubinsky, Boris (22 September 2021). "Isochoric supercooled preservation and revival of human cardiac microtissues". Communications Biology. 4 (1): 1118. doi:10.1038/s42003-021-02650-9. ISSN 2399-3642. PMC 8458396. PMID 34552201.
  4. ^ Ward, Alyssa; Klassen, David K.; Franz, Kate M.; Giwa, Sebastian; Lewis, Jedediah K. (June 2018). "Social, economic, and policy implications of organ preservation advances". Current Opinion in Organ Transplantation. 23 (3): 336–346. doi:10.1097/MOT.0000000000000532. PMC 5959266. PMID 29683801.