An ideal gas is taken from state C to state D along two alternative paths:
• Path A (reversible): The gas absorbs 700 J of energy as heat from a reservoir at 350 K while expanding isothermally.
• Path B (irreversible): The gas absorbs the same 700 J of energy as heat from a 700 K reservoir in a free expansion and then equilibrates to state D without further heat exchange.
For each path, calculate (i) the entropy change of the gas, (ii) the entropy change of the surroundings, and (iii) the total entropy change for the universe. Which path produces the greater increase in the universe’s entropy?