Graphs of thermodynamic transformations I received a question from one of my students of a high school (17 years old) with reference to a graph of a Clayperon-plane. Suppose that it is the one shown in the figure.

From state $A \to B$ is evidently an isobar (with volume expansion); and from $B\to C$ an isochore.

Are the transformations from $C\to D$ and from $D \to A$ hypothetical or not real transformations referring to ideal gases or to real gases or are they approximations of particular thermodynamic transformations that I am not known to except for adiabatic, isothermal, isochore and isobaric? What is the best justification that I can give my students of a high school about transformations such as those going from $C$ to $D$ and from $D$ to $A$?

 A: 
What is the best justification that I can give my students of a high
school about transformations such as those going from $C$ to $D$ and
from $D$ to $A$?

For one, you can say that not all processes necessarily have a name and need not be either isobaric, isochoric, isothermal, adiabatic. It so happens that in the case of an ideal gas these processes are specific cases for what is called a polytropic process, which is given by
$$pV^{n}=C$$
Where $n$ is called the polytropic index (not to be confused with $n$ being the number of moles of a gas) and $C$ is a constant. Each of the four processes mentioned can be derived from the polytropic process with the selection of an appropriate value of $n$. (See https://en.wikipedia.org/wiki/Polytropic_process).
This is not to say that C to D and D to A are even possible in the form of a single "process". But perhaps by including multiple equilibrium states along each path it may be possible to break each path down to a combination of multiple polytropic processes which applicable values of $n$ connecting the equilibrium states. Might be an interesting student exercise.
Hope this helps.
