Step 1: Understanding the Concept:
A Carnot engine is an ideal, reversible thermodynamic cycle whose efficiency depends purely on the temperatures of the hot and cold thermal reservoirs.
Step 2: Key Formula or Approach:
The efficiency \(\eta\) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T_C}{T_H} \]
where \(T_C\) is the temperature of the cold reservoir and \(T_H\) is the temperature of the hot reservoir.
To express it as a percentage:
\[ \eta (%) = \left( 1 - \frac{T_C}{T_H} \right) \times 100 \]
Step 3: Detailed Explanation:
Given values are:
Hot reservoir temperature (steam point), \(T_H = 373 \text{ K}\).
Cold reservoir temperature (ice point), \(T_C = 273 \text{ K}\).
Substituting the values into the formula:
\[ \eta = 1 - \frac{273}{373} \]
\[ \eta = \frac{373 - 273}{373} = \frac{100}{373} \]
\[ \eta \approx 0.26809 \]
Converting to percentage:
\[ \eta (%) = 0.26809 \times 100 \approx 26.8% \]
Step 4: Final Answer:
The efficiency of the Carnot engine is \(26.8%\).