Question

An engine operating between the boiling and freezing points of water will have 
A. efficiency more than 27%  
B. efficiency less than the efficiency a Carnot engine operating between the same two temperatures.  
C. efficiency equal to 27%  
D. efficiency less than 27% 

• A. B and C only
• B. B and D only
• C. A and B only
• D. B, C and D only

Answer 1

The Correct Option is B

To solve this question, we need to understand the concept of efficiency of an engine operating between two temperatures and compare it with the Carnot engine's efficiency, which is the maximum possible efficiency for a heat engine operating between two given temperatures.

The efficiency, \eta, of a Carnot engine is given by the formula:

\eta = 1 - \frac{T_C}{T_H},

where T_H is the absolute temperature of the hot reservoir and T_C is the absolute temperature of the cold reservoir. In this problem:

• The boiling point of water (T_H) is 100°C, which is 373 K.
• The freezing point of water (T_C) is 0°C, which is 273 K.

So, the efficiency of a Carnot engine operating between these two temperatures can be calculated as:

\eta_{\text{Carnot}} = 1 - \frac{273}{373} = 1 - 0.732 \approx 0.268

This approximates to an efficiency of 26.8%.

Now, let's analyze the provided options:

• A. Efficiency more than 27%: The efficiency of the Carnot engine is already less than 27%, so it's impossible for any real engine, which is less efficient than the Carnot engine, to have more than 27% efficiency. Therefore, this option is incorrect.
• B. Efficiency less than the efficiency of a Carnot engine operating between the same two temperatures: Since no real engine can exceed the Carnot efficiency, this option is logically correct.
• C. Efficiency equal to 27%: This is not possible as the Carnot efficiency itself is approximately 26.8%. Real engines always have efficiencies less than the Carnot efficiency. Therefore, this option is incorrect.
• D. Efficiency less than 27%: As calculated, the Carnot efficiency is less than 27%, and such must also be the case for any real engine. This option is correct.

Therefore, the correct answer is B and D only.