Final answer:
The maximum theoretical efficiency of a heat engine, such as in a nuclear or coal-fired power plant, can be calculated using the Carnot efficiency formula. The temperatures must be converted to Kelvin before applying the formula. This concept is essential in the fields of thermodynamics and energy efficiency.
Step-by-step explanation:
The question pertains to the calculation of the maximum theoretical efficiency of a heat engine, specifically within the context of a nuclear or coal-fired power plant. The efficiency of such a heat engine is determined using the Carnot efficiency formula, which is Efficiency (Effc) = 1 - (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir, with both temperatures being in Kelvin.
To calculate the efficiency, temperatures given in the question first need to be converted from Celsius to Kelvin. The formula for that conversion is K = °C + 273.15. For example, a nuclear power reactor operating between the temperatures of 300°C and 27°C would have a theoretical maximum efficiency calculated by converting these temperatures to Kelvin and then applying the Carnot efficiency formula.
Applying this to a steam engine or power plant, you would calculate the efficiency based on the operating temperatures of steam (for instance, 450°C steam and 270°C exhaust for the first engine in a practical steam engine scenario). For the given coal-fired electrical power station with a steam temperature of 550°C and environment temperature of 20°C, you calculate its percentage of the maximum efficiency similarly, after converting these temperatures to Kelvin.