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Isochoric process : ウィキペディア英語版
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. The isochoric process here should be a quasi-static process.
==Formalism==
An isochoric thermodynamic process is characterized by constant volume, i.e., \Delta V = 0 .
The process does no pressure-volume work, since such work is defined by
: \Delta W = P \Delta V ,
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.〔https://www.physicsforums.com/threads/if-gas-volume-remains-constant-it-can-does-work-to-others.765131/〕
For a reversible process, the first law of thermodynamics gives the change in the system's internal energy:
:dU = dQ - dW
Replacing work with a change in volume gives
:dU = dQ - PdV
Since the process is isochoric, dV = 0, the previous equation now gives
:dU = dQ
Using the definition of specific heat capacity at constant volume,
:C_v = dU/dT,
:dQ = m c_v dT
Integrating both sides yields
:\Delta Q\ = m\int_^ \! c_v \, dT.
Where c_v is the specific heat capacity at constant volume, T_1 is the initial temperature and T_2 is the final temperature. We conclude with:
:\Delta Q\ = m c_v \Delta T\
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.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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