When does work equal zero in a thermodynamic process?

Work is defined in thermodynamics as the energy transferred when a force is applied to move an object. In the context of a gas within a cylinder, for example, work is related to volume changes—specifically, it is done by the gas when it expands or is compressed. The relationship can be described by the equation for work (W) in a pressure-volume system:

[ W = P \Delta V ]

where ( P ) is the pressure and ( \Delta V ) is the change in volume.

When the volume is constant, meaning there is no change in volume (( \Delta V = 0 )), the work done is zero because there is no displacement occurring. In other words, if a system does not change in volume, then the system isn't pushing against any external pressure to perform work.

Understanding this concept allows us to see why work would not equal zero in the other scenarios. Heat transfer does not inherently correlate with work being done. Work being zero is not a result of constant pressure but rather a result of no volume change. Temperature being high also does not dictate the performance of work; it's more about the interactions and energy state of the system rather than a direct connection with work being done. Thus,