Physics
Physics
Problem
An insulated cylinder contains an ideal monatomic gas at temperature 300 K and volume . Two different processes take the gas to a final volume while the cylinder remains thermally insulated from the surroundings. Process A: The piston is moved outward extremely slowly so that the gas remains essentially in internal equilibrium at every stage. Process B: The piston is suddenly removed, allowing the gas to expand freely into the new volume. Assume the gas behaves ideally throughout and that no energy crosses the system boundary as heat or work except that associated with the piston motion described above. a. For each process, describe qualitatively how the entropy of the gas changes between the initial and final states. b. For each process, discuss whether any entropy change occurs in the surroundings. Justify your answer. c. For each process, determine the sign (positive, negative, or zero) of the total entropy change of the universe and explain what this implies about the reversibility of the process.Intuitive explanation
The key is recognizing that both processes are adiabatic (no heat exchange), but they differ fundamentally in how the gas does work. Process A is a quasi-static adiabatic expansion where the gas does work against the piston and cools down; Process B is a free expansion where the gas does no work at all, so internal energy stays constant and temperature doesn't change. Even though both start and end at the same volumes, the final temperatures will differ because the paths dissipate energy differently—one reversibly, one irreversibly.
Intuitive explanation
The key is recognizing that both processes are adiabatic (no heat exchange), but they differ fundamentally in how the gas does work. Process A is a quasi-static adiabatic expansion where the gas does work against the piston and cools down; Process B is a free expansion where the gas does no work at all, so internal energy stays constant and temperature doesn't change. Even though both start and end at the same volumes, the final temperatures will differ because the paths dissipate energy differently—one reversibly, one irreversibly.