Final answer:
To find the maximum theoretical efficiency for a heat engine, like in a nuclear power plant scenario, one applies the Carnot efficiency formula by converting the high and low operational temperatures to Kelvins and then following the formula Effc = 1 - (Tc/Th). For temperatures of 300°C and 27°C, this results in an efficiency of 47.65%.
Step-by-step explanation:
The question revolves around the concept of thermodynamics and how it applies to practical heat engines and electrical power generation. By considering a nuclear power reactor with water at high temperature and steam condensing at a lower temperature, the maximum theoretical efficiency for a heat engine can be calculated.
In general, the Carnot efficiency formula, which is Effc = 1 − (Tc/Th), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir in Kelvins, can be used to calculate the maximum theoretical efficiency of a heat engine. To get the efficiency, we first convert the temperatures from degrees Celsius to Kelvins (by adding 273.15 to each temperature). For a nuclear reactor operating between a high temperature of 300°C (573.15K) and a low temperature of 27°C (300.15K), the theoretical efficiency is calculated using the Carnot efficiency formula.
The calculation would result in the following:
- Convert temperatures from Celsius to Kelvin: Th = 300 + 273.15 = 573.15 K, Tc = 27 + 273.15 = 300.15 K.
- Plug into the Carnot efficiency formula: Effc = 1 − (Tc/Th) = 1 − (300.15/573.15).
- Calculate the efficiency: Effc = 1 − 0.5235 = 0.4765 or 47.65%.
This would be the maximum theoretical efficiency of the cycle, not accounting for real-world losses that would make actual efficiency lower.