Two researchers compress identical samples of ideal monatomic gas from an initial state S(Pi=1.0atm,Vi=2.0L,Ti=300K) to a final pressure of 4.0atm.
• Researcher X performs the compression very slowly while the cylinder remains in thermal contact with a large reservoir at 300K.
• Researcher Y performs the compression rapidly in a cylinder whose walls are perfectly insulating.
Assume the gas behaves ideally in both experiments.
(a) Sketch qualitatively distinct P–V curves that represent the two compression paths on the same set of axes. Label the curve produced by each researcher.
(b) For each compression, identify the thermodynamic process type. Support your answer with reference to the experimental conditions.
(c) Derive an expression for the final temperature Tf reached in researcher Y’s compression, expressing your result in terms of Ti, Pi, and Pf only.
(d) Compare the magnitude of the work done ON the gas in the two compressions. State which is greater and justify your conclusion using properties of the respective P–V paths.