Question

If the temperature of a hot reservoir is 600K and the cold reservoir is 300K, the efficiency of the Carnot engine is:

• A. 25%
• B. 75%
• C. 50%
• D. 100%

Hint:

Always verify that the given temperatures are in Kelvin (K) before using the Carnot efficiency formula.
If they are provided in Celsius, you must convert them by adding 273.15.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
A Carnot engine is a theoretical thermodynamic cycle that determines the maximum possible efficiency any heat engine can achieve.
The efficiency depends exclusively on the absolute temperatures of the hot and cold reservoirs.

Step 2: Key Formula or Approach:
The formula for the efficiency of a Carnot engine is \( \eta = 1 - \frac{T_C}{T_H} \).
Here, \( T_C \) is the absolute temperature of the cold reservoir and \( T_H \) is the absolute temperature of the hot reservoir.

Step 3: Detailed Explanation:
From the given question, the temperature of the hot reservoir is \( T_H = 600 \text{ K} \).
The temperature of the cold reservoir is \( T_C = 300 \text{ K} \).
Substitute these temperature values into the efficiency formula:
\[ \eta = 1 - \frac{300}{600} \]
\[ \eta = 1 - \frac{1}{2} \]
\[ \eta = 0.5 \]
To convert this decimal to a percentage, multiply by 100:
\[ \text{Efficiency \%} = 0.5 \times 100\% = 50\% \]

Step 4: Final Answer:
The efficiency of the Carnot engine is 50%, which corresponds to option (C).