# Isochoric

 A PV diagram depiction of a isochoric process or isochoric transformation.
In thermodynamics, isochoric, from Greek (ἴσος) iso-, meaning “equal, homogeneous, uniform”, + Greek (χώρα) -chora, meaning “place, space” (Waser, 1966), "isometric" (synonym) or isochore, is a transformation (or process) of a body (or system) that proceeds at constant volume.

Overview
The following relation defines the basic meaning of isochoric: [1]

V = constant

A typical exam question asked, in the context of isochoric processes, is how much work does the body perform when it is heated at constant volume such that its pressure increases? The answer is that, by definition of work, as a body or region of boundary moved through a distance by a force, no work is performed. [2]

A transformation in which the system performs no external work is called an isochore transformation, or isochoric process, meaning that the volume was constant during the transformation, hence the integral for PV work:

$W = \int_{V_1}^{V_2} PdV \,$

is zero because dV is zero, or by integration, V = a constant. [3]

Isothermal
Isobaric
Isentropic

References
1. (a) Fermi, Enrico. (1936). Thermodynamics (pg. 7). Dover.
(b) Potter, Merle C. and Somerton, Craig W. (2009). Schaum's Outlines: Thermodynamics for Engineers (pg. 5). McGraw-Hill.
2. Holzner, Steven. (2007). Physics Workbook for Dummies (Constant Volume: Isochoric Processes, pg. 253). For Dummies.
3. Fermi, Enrico. (1936). Thermodynamics (pg. 7). Prentice-Hall.