(a) What is meant by the term state function? (b) Give an example of a quantity that is a state function and one that is not. (c) Is the volume of a system a state function? Why or why not?

A state function is a property of a system that depends only on its current state, which is determined by factors such as temperature, pressure, and composition, and not on the path taken to achieve that state. In other words, state functions are independent of the process or the history of the system.

An example of a state function is the internal energy of a system (U). It is a state function because it only depends on the current state of the system and not how we reached that state. Suppose we change the temperature of a gas, the final internal energy of the gas is the same regardless of whether we heated it quickly or slowly, in steps or continuously. On the other hand, heat (q) and work (w) are examples of non-state functions or process functions. They depend on the specific process or pathway taken to reach a particular state. Suppose we have a system going from an initial state to a final state; the heat and work would be different if the process was done isothermally (i.e., at constant temperature) or adiabatically (i.e., no heat exchange).

The volume of a system (V) is a state function because it only depends on the current state of the system and not on the history or process taken to reach that state. For example, if a gas is compressed to half its initial volume, the final volume is the same, regardless of whether the compression was done slowly or quickly, or even in a multistep process. The volume only depends on the current pressure, temperature, and composition of the system and is, therefore, a state function.