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.

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.^{[citation needed]} The sign convention is such that positive work is performed by the system on the environment.^{[citation needed]}

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 gives the change in the system's internal energy: $${\displaystyle dU=dQ-dW}$$

Replacing work with a change in volume gives $${\displaystyle dU=dQ-P\,dV}$$

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, c_v = (dQ/dT)/m, where m is the mass of the gas, we get $${\displaystyle dQ=mc_{\mathrm {v} }\,dT}$$

Integrating both sides yields $${\displaystyle \Delta Q\ =m\int _{T_{1}}^{T_{2}}\!c_{\mathrm {v} }\,dT,}$$ 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: $${\displaystyle \Delta Q\ =mc_{\mathrm {v} }\Delta T}$$