Final answer:
The student's question pertains to the thermodynamic processes experienced by a gas during a cycle, and how these processes can be represented on P-V, T-V, and T-S diagrams. It includes constant pressure expansion, a polytropic process, and a constant temperature process.
Step-by-step explanation:
The student's question involves thermodynamic processes where a given quantity of gas undergoes expansion and contraction through a series of steps that include constant pressure, polytropic, and constant temperature processes. A sketch of these processes will illustrate the changes in pressure, volume, and temperature on different thermodynamic diagrams such as P-V (pressure-volume), T-V (temperature-volume), and T-S (temperature-entropy).
The initial state of the gas at 206°C and 7 bar which expands at constant pressure would appear as a horizontal line on the P-V diagram as pressure remains constant while volume increases. The polytropic process with an index of 1.5 would be represented by a curve that is steeper than an isotherm, indicating a change in temperature as well as volume, whereas the constant temperature process will appear as a horizontal line on the T-V diagram and as an isotherm on the P-V diagram.
These diagrams are useful tools for visualizing and understanding the different states and transformations that the gas undergoes throughout the cycle. The detailed sketches would require numerical values and calculations which are beyond the scope of this answer but can be deduced by applying the ideal gas law and the polytropic process equations.