The maximum theoretical efficiency of a heat engine operating between reservoir temperatures of 25°C and 300°C is approximately 47.99% after converting the given temperatures to kelvins and applying the Carnot efficiency formula.
Step-by-step explanation:
The student asks about the maximum efficiency for a heat engine that operates between two reservoirs at temperatures of 25°C and 300°C. To calculate the maximum efficiency, which is the Carnot efficiency, we need to convert these temperatures to kelvins. The formula for the Carnot efficiency is ì = 1 - (Tc/Th), where Tc is the cold reservoir temperature and Th is the hot reservoir temperature in kelvins.
First, we convert the given temperatures to kelvins:
The cold reservoir temperature (25°C) is Tc = 25 + 273.15 = 298.15 K.
The hot reservoir temperature (300°C) is Th = 300 + 273.15 = 573.15 K.
Using these temperatures, the maximum efficiency can be calculated:
ì = 1 - (Tc/Th) = 1 - (298.15/573.15) = 1 - 0.5201 = 0.4799 or 47.99%
Therefore, the maximum theoretical efficiency of the heat engine is approximately 47.99%.
The probable question can be: A heat engine operates between two reservoirs at temperatures of 25°C and 300°C. What is the maximum
eficiency for this engine?