Question

Calculate the efficiency of a Carnot engine operating between the steam point (373 K) and ice point (273 K).

• A. 26.8%
• B. 36.8%
• C. 46.8%
• D. 56.8%

Hint:

Remember: $\eta = 1 - \frac{T_c}{T_h}$ (Temperatures must be in Kelvin).

Answer 1

The Correct Option is A

Concept: Efficiency of a Carnot engine depends only on the temperatures of the hot and cold reservoirs.
Step 1: Formula for Carnot efficiency.
\[ \eta = 1 - \frac{T_c}{T_h} \]
Step 2: Substituting values.
\[ T_h = 373\,K, \quad T_c = 273\,K \] \[ \eta = 1 - \frac{273}{373} \]
Step 3: Calculation.
\[ \frac{273}{373} \approx 0.732 \] \[ \eta = 1 - 0.732 = 0.268 \]
Step 4: Convert to percentage.
\[ \eta = 26.8% \]
Step 5: Evaluating the options.

• 26.8% $\rightarrow$ Correct
• 36.8% $\rightarrow$ Incorrect
• 46.8% $\rightarrow$ Incorrect
• 56.8% $\rightarrow$ Incorrect

Step 6: Conclusion.
Thus, the efficiency of the Carnot engine is 26.8%.