Question

Work done in an isochoric process is always?

Answer 1

In an isochoric process, also known as an isovolumetric process, the volume of a system remains constant. In such a process, the work done is always zero.
Work is defined as the energy transferred to or from a system due to the application of a force over a displacement. In an isochoric process, since there is no change in volume, there is no displacement of the system's boundaries, and therefore no work is done. The force may be applied, but if there is no displacement, the work done is zero.
Mathematically, the work done (W) in a process is given by the equation:
$W = ∫F·dx$
where F is the applied force and dx is the displacement.
Since dx is zero in an isochoric process, the integral becomes zero, resulting in no work done.
It's important to note that although no work is done in an isochoric process, heat can still be exchanged with the surroundings, resulting in changes in the system's internal energy. The internal energy change corresponds to the heat transfer into or out of the system.