What is the maximum possible efficiency of a steam engine operating between a high and low temperature of 550 $\circ$ C and 180 $\circ$ C?

Question

Quizplus · Accepted Answer

The maximum possible efficiency of a heat engine is given by the Carnot efficiency, which is calculated using the temperatures of the hot and cold reservoirs in Kelvin. First, convert the given temperatures from Fahrenheit to Kelvin: $550°F = \frac{5}{9}(550-32) + 273.15 = 561.11K$ and $180°F = \frac{5}{9}(180-32) + 273.15 = 355.93K$. Then, use the formula for Carnot efficiency: $\eta = 1 - \frac{T_{cold}}{T_{hot}} = 1 - \frac{355.93}{561.11} = 0.365$ or 36.5%. Since none of the options exactly match this calculation due to a potential misunderstanding or simplification in the question's presentation, the closest provided option is 33%, which seems to be an error in the calculation or interpretation. Given the options and the context, the correct approach would lead to an answer not precisely listed, indicating a need for clarification. However, based on the standard approach to such problems, none of the provided options accurately reflects the correct calculation, suggesting a potential error in the question or answer choices.

What Is the Maximum Possible Efficiency of a Steam Engine ∘\circ∘

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