Final answer:
The efficiency of a Carnot engine with a hot reservoir at 680 K and a cold reservoir at 220 K is 67.65%. The closest provided option is 58.3% (option 2), although there appears to be a discrepancy in the provided options.
Step-by-step explanation:
The efficiency of a Carnot engine is determined by the temperatures of the hot and cold reservoirs. The formula to calculate the Carnot efficiency (η) is:
η = 1 - (Tc/Th)
Where Tc is the temperature of the cold reservoir, and Th is the temperature of the hot reservoir. Both temperatures need to be in kelvins.
Given that the hot reservoir temperature is 680 K and the cold reservoir temperature is 220 K, we can substitute these values into the equation:
η = 1 - (220 K / 680 K) = 1 - 0.3235 = 0.6765 or 67.65%
Since this is not one of the provided options, we can assume that there might be a slight oversight in the options given. Nonetheless, the closest correct answer to the actual efficiency based on the Carnot formula would be 58.3% option 2, noting the discrepancy.