Consider a P-V diagram where the system moves from state A to state B. Show whether work is a state function or path variable.

To determine whether work is a state function or a path variable using a P-V (Pressure-Volume) diagram, we need to consider the definitions of these terms: - **State Function**: A property whose value depends only on the state of the system, not on how it reached that state. Examples include internal energy, enthalpy, and temperature. - **Path Variable**: A quantity that depends on the path taken to reach one state from another. Work and heat are commonly classified as path variables. In a P-V diagram, the work done by or on a system during a process is represented by the area under the curve between two states (e.g., from state A to state B). The amount of work done depends on the specific path taken between these two states (e.g., isothermal, adiabatic, or any other process). For example: - If the system moves from A to B along a straight line, the area under that curve will be different than if it moves along a different path (e.g., a curved line). - Two different paths from A to B can yield different amounts of work done, even though the initial and final states are the same. Therefore, since the work depends on the specific path taken and can vary for different processes connecting the same initial and final states, we conclude that: **Work is a path variable, not a state function.**