An engine operating between the boiling and freezing points of water will have
A. efficiency more than 27%.
B. efficiency less than the efficiency of a Carnot engine operating between the same two temperatures.
C. efficiency equal to 27 %
D. efficiency less than 27 %
Choose the correct answer from the options given below:

Solution

Physics sir · 2 steps

Find the Carnot limit first; between 373 K and 273 K no engine can reach even 27%.

1. Use kelvin. The boiling point of water is T_H = 373 K and the freezing point is T_C = 273 K. The Carnot efficiency between them is the highest any engine can reach.

   η_(Carnot) = 1 - T_C/T_H = 1 - 273/373 = 100/373 ≈ 0.268 = 26.8%

   Statement	Check	Verdict
   A: more than 27%	Beats the Carnot limit of 26.8%	false
   B: less than Carnot	A real engine is irreversible, so it falls below the Carnot value	true
   C: equal to 27%	Even the ideal engine only reaches 26.8%	false
   D: less than 27%	Any efficiency up to 26.8% is below 27%	true

2. So. Only B and D hold, which is option (b).

The idea to keep. For any engine question, first work out 1 - T_C/T_H with temperatures in kelvin. That is the ceiling, and a real engine always stays below it.

Answer from the NTA final answer key. Solution by PrepWiser.