A sealed rigid cylinder contains an ideal gas initially at a uniform temperature of 500 K. The cylinder is surrounded by a large thermal reservoir that remains at 300 K. The gas is allowed to reach equilibrium with the reservoir by one of two alternative procedures:
• Process A: The gas drives a perfectly reversible heat engine that delivers mechanical work while the gas cools to 300 K.
• Process B: The cylinder is simply placed in thermal contact with the reservoir so that the gas cools directly to 300 K with negligible work output.
Assume the initial and final thermodynamic states of the gas are identical in the two processes, and ignore any changes in kinetic or potential energy.
(a) Describe qualitatively how the total entropy of the gas-plus-reservoir system changes during each process.
(b) Explain why the maximum amount of useful work obtainable from the gas differs between Process A and Process B even though the initial and final states of the gas are the same.
(c) Identify the key thermodynamic quantities that determine the upper limit on useful work that can be extracted as the gas cools.
(d) Describe two practical design strategies engineers employ to make real devices approach the upper limit you identified in part (c).