Isochoric 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

${\displaystyle W=P\Delta V}$,

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.[1]

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

${\displaystyle dU=dQ-dW}$

Replacing work with a change in volume gives

${\displaystyle dU=dQ-PdV}$

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

${\displaystyle dU=dQ}$

Using the definition of specific heat capacity at constant volume,

${\displaystyle C_{v}={\frac {dU}{dT}}}$,

${\displaystyle dQ=mc_{v}\,dT}$

Integrating both sides yields

${\displaystyle \Delta Q\ =m\int _{T_{1}}^{T_{2}}\!c_{v}\,dT.}$

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

${\displaystyle \Delta Q\ =mc_{v}\Delta T\ }$

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.

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."

• Isobaric process
• Adiabatic process
• Cyclic process
• Isothermal process
• Polytropic process