From Andrew Zimmerman Jones,
Your Guide to Physics.
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Definition: An isochoric process is a thermodynamic process in which the volume remains constant. Since the volume is constant, the system does no work and W = 0.

This is perhaps the easiest of the thermodynamic variables to control, since it can be obtained by placing the system in a sealed container which neither expands nor contracts.

Applying the first law of thermodynamics to this situation, we find that:

delta-U = Q

Since delta-U is the change in internal energy and Q is the heat transfer into or out of the system, we see that all of the heat either comes from internal energy or goes into increasing the internal energy.

Constant Volume, But W is Non-zero

It is actually possible to do work on a system without changing the volume, as in the case of stirring a liquid. Some sources use "isochoric" in these cases to mean "zero-work" regardless of whether there is a change in volume or not. In most straightforward applications, however, this nuance will not need to be considered ... if the volume remains constant throughout the process, it is an isochoric process.