Final answer:
The coal-fired electrical power station obtains approximately 59% of the maximum efficiency according to the Carnot efficiency formula, given the steam temperature of 550ºC and an environmental temperature of 20ºC. None of the options are correct.
Step-by-step explanation:
The student has asked what percentage of the maximum efficiency a coal-fired electrical power station with an actual efficiency of 38% achieves. The temperature of the steam leaving the boiler is 550ºC and the environmental temperature is assumed to be 20ºC.
Using the Carnot efficiency formula for maximum efficiency, which is Efficiency (max) = 1 - (Tc/Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature, we calculate the maximum possible efficiency. First, we convert the given temperatures from Celsius to Kelvin by adding 273.15.
Th = 550ºC + 273.15 = 823.15 K
Tc = 20ºC + 273.15 = 293.15 K
The maximum efficiency is then:
Efficiency (max) = 1 - (Tc/Th) = 1 - (293.15/823.15) = 1 - 0.356 = 0.644 or 64.4%
Therefore, the percentage of the maximum efficiency this station obtains is:
(Actual Efficiency / Maximum Efficiency) × 100% = (38% / 64.4%) × 100% ≈ 59%