A fixed amount of ideal monatomic gas is used in three separate laboratory demonstrations, each beginning at the same initial state (state i) and ending at a different final state (state f). For every demonstration, the surroundings are at atmospheric pressure.
Demonstration A: The gas is rapidly compressed by a motor–driven piston while the cylinder walls are perfectly insulated.
Demonstration B: The gas expands slowly against a movable piston while being kept in thermal contact with a large ice–water bath that maintains a constant temperature.
Demonstration C: With the piston locked in place, the gas is electrically heated by a coil until its pressure doubles.
Assume any kinetic energy of the piston is negligible once each process is complete.
(1) For each demonstration, indicate whether the energy transferred by heating Q, the work done on the gas W, and the change in internal energy ΔU are positive, negative, or zero. Justify every sign you assign by explicitly referencing the direction of each energy transfer.
(2) Rank the magnitudes ∣Q∣, ∣W∣, and ∣ΔU∣ for Demonstration B only, from greatest to least. Provide clear reasoning connected to the physical constraints described.
(3) For Demonstration C, describe qualitatively how the average random kinetic energy of the gas molecules changes and explain how this relates to the sign of ΔU. Connect your explanation to the microscopic interpretation of internal energy.