Question

The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincide and Kelvin-Fahrenheit scales coincide is (approximately):

• A. \( 45% \)
• B. \( 35% \)
• C. \( 60% \)
• D. \( 50% \)

Hint:

The efficiency of a heat engine operating between two temperatures is given by \( \eta = 1 - \frac{T_C}{T_H} \). Ensure temperature values are converted to Kelvin before substitution.

Answer 1

The Correct Option is C

Step 1: Understanding the Given Temperatures - The Celsius-Fahrenheit coincidence occurs at: \[ T_1 = -40^\circ C = 233 \text{ K}. \] - The Kelvin-Fahrenheit coincidence occurs at: \[ T_2 = 574.25 \text{ K}. \] 
Step 2: Applying Carnot’s Efficiency Formula The efficiency of a Carnot engine is given by: \[ \eta = 1 - \frac{T_C}{T_H}. \] Substituting values: \[ \eta = 1 - \frac{233}{574.25}. \] \[ \eta = 1 - 0.4059. \] \[ \eta = 0.594 \approx 60%. \] Thus, the correct answer is:  60%.