Question

The efficiency of an ideal heat engine working between the freezing point and boiling point of water, is

• A. 0.125
• B. 26.8 %
• C. 6.25 %
• D. 0.2

Answer 1

The Correct Option is B

To determine the efficiency of an ideal heat engine working between the freezing and boiling points of water, we can use the Carnot efficiency formula. The efficiency (\(\eta\)) of a Carnot engine is given by:

\(\eta = 1 - \frac{T_C}{T_H}\)

where:

• \(T_C\) = Absolute temperature of the cold reservoir (freezing point of water)
• \(T_H\) = Absolute temperature of the hot reservoir (boiling point of water)

The freezing point of water is 0°C, which is 273.15 Kelvin, and the boiling point of water is 100°C, which is 373.15 Kelvin.

Now, plug the values into the formula:

\(\eta = 1 - \frac{273.15}{373.15}\)

Calculating the above expression:

\(\frac{273.15}{373.15} = 0.7323\)

\(\eta = 1 - 0.7323 = 0.2677\)

Converting this to a percentage:

\(\eta = 0.2677 \times 100 = 26.77\%\)

This result is approximately 26.8%.

Therefore, the efficiency of an ideal heat engine operating between the freezing and boiling points of water is 26.8%. This matches the correct answer option given.

Thus, the correct answer is: 26.8%