Final answer:
The net work done by R1 is indeed greater than the work done by R2, but the efficiencies of R1 and R2 are equal because they are both reversible engine cycles operating between the same thermal reservoirs.
Step-by-step explanation:
Considering two reversible power cycles R1 and R2 operating between the same two hot and cold thermal reservoirs at temperatures of 1000 K and 500 K respectively, with the work output from power cycle R1 being three times more than the work output of cycle R2, we need to analyze their efficiencies and work output. From the second law of thermodynamics, it is known that all reversible engine cycles have the same efficiency when operating between two specific reservoirs. Therefore, here are the correct statements:
- The net work done by R1 is greater than the net work done by R2 (statement c) because R1 does three times the work of R2.
- The efficiency of R1 is not higher than the efficiency of R2 (statement a) since both are reversible cycles operating between the same reservoirs, hence have the same efficiency.
- The Carnot efficiency for R1 is the same as the Carnot efficiency for R2 (statement b) because, by definition, all reversible engines between the same two reservoirs have the same efficiency.
- The thermal efficiency of R1 is equal to the thermal efficiency of R2 (statement d), following the same logic that all reversible cycles between the same two reservoirs have identical efficiencies.