A vertical cylinder fitted with a frictionless, massless piston contains an ideal mono-atomic gas initially in mechanical and thermal equilibrium with the laboratory at 300 K.
The experimenter performs two consecutive procedures:
• Step 1 – She places an electric heater under the cylinder base. The heater transfers 200 J of energy to the gas while the piston is free to move. The cylinder walls are good thermal conductors, so any energy that leaves or enters the gas must do so through the base or the piston face.
• Step 2 – Immediately after Step 1, she encloses the entire cylinder–heater assembly inside a rigid, perfectly insulating shell and disconnects the heater from the power supply. No further energy or matter can cross the shell once it is sealed.
Answer the following, giving clear reasoning grounded in thermodynamic principles.
(a) For Step 1, identify whether the gas alone constitutes an isolated, closed, or open system. Justify your classification in terms of possible transfers of energy and matter across the system boundary.
(b) During Step 1, state whether the entropy of the gas increases, decreases, or remains unchanged. Explain your answer qualitatively—do not perform calculations.
(c) For Step 2, consider the composite of "gas + cylinder + heater" as the system. Classify this new system type and predict the sign of its total entropy change as it evolves to a final equilibrium after sealing. Support your prediction with appropriate reasoning.
(d) Compare the direction of entropy change of the surroundings (everything external to the composite system) in Step 1 with that in Step 2. Discuss how the choice of system boundary influences your conclusions about the second law.