What happens to work done if the volume remains constant?

When the volume remains constant during a process, the work done on or by the system is considered to be zero. This is derived from the thermodynamic definition of work, which for processes involving gases is given by the equation:

[ W = -P \Delta V ]

where ( W ) is the work done, ( P ) is the pressure, and ( \Delta V ) is the change in volume. If the volume does not change (i.e., ( \Delta V = 0 )), then the equation simplifies to:

[ W = -P \times 0 = 0 ]

This indicates that regardless of the pressure or any other conditions, if the volume of the system does not change, no work is done. This scenario is common in isochoric processes, where the system's volume remains constant, typically in rigid containers. Therefore, saying that the work done is zero accurately reflects the physical situation.