Still from multimedia explanation of State Functions in Physical chemistry textbook

Section 2.2 of the Physical Chemistry textbook, States and State Functions, provides a wonderful definition for two terms that are often understood but difficult to define.  The use of simplistic terminology and multimedia examples help to clarify the meanings.
The key to understanding state functions, as pointed out in the text, is understanding the dependence of the individual variables on the pathway.  Some key variables worth exploring are:  temperature, mass, pressure, volume, energy and work.
The ultimate question in determining whether a variable is a state function is:  Do I care how I got the final value?
Let’s discuss the temperature drop as seen in the multimedia clip.  The addition of the ice cube lowered the overall temperature of the liquid by a fixed number.  Would the final temperature have been any different if it had been broken into three smaller ice cubes?  What if the three smaller ice cubes were added at different times?  What if it had been placed in a cooler instead of adding ice?  As long as the final temperature in each case is the same, it does not matter how the cooling was done.  Thus temperature is a state function.
Now consider mass, pressure and volume.  When weighing an object, does it matter how much it weighed one minute, one hour or a year ago?  What about pressure and volume?  Each of these variables relies only on the final state, not on the “pathway” and are examples of state functions.
The final two variables mentioned earlier are work and energy.  Before determining whether they are state functions, a vital question must be answered:  What is the difference between work and energy?  A simplistic definition of energy is the capacity to do work using the energy of motion, kinetic, or the conversion of stored energy, potential.  Work on the other hand is the actual use of energy to perform a specific task.
Again let’s use the multimedia example of the ladybug to compare them.  The lady bug has two different “pathways” to follow.  In each case, the final destination is the same but how does that relate to work and energy?  Let’s consider the journey in terms of energy.  Initially the ladybug is at rest or has potential energy but no kinetic energy.  In order to travel it must convert some of its potential into kinetic energy.  Some of the kinetic energy is then “converted” into work to travel from one destination to the other.  Once at the final destination, the ladybug is again at rest with a fixed amount of potential energy.

Still from animation explaining State function in Physical chemistry (click to enlarge)

While the overall potential energy might be less than at the beginning, do you care how it lost that energy or only in the final amount that could be used in the future?   Again, the final value is all that is important and thus, energy is also a state function.
Work, though, is quite different.  When determining the final amount of work done, does it matter which pathway the ladybug took?  In each case, a different amount of energy was converted into work so each pathway has a different value.  Work therefore is not a state function and the pathway must be considered.
A useful comparison is destination vs. distance.  Destination, like energy is fixed while distance, like work, depends on the path traveled.
The example of the density of water at 25^◦C and fixed pressure is a wonderful way to explore the application of state functions using an already familiar concept.  The multimedia, examples and easily understandable explanations really illustrate the meaning of state functions.