Question

A Carnot engine works between \(600\,\text{K}\) and \(300\,\text{K}\). Find its efficiency.

• A. \(25\%\)
• B. \(40\%\)
• C. \(50\%\)
• D. \(60\%\)

Hint:

Carnot efficiency depends only on temperatures of reservoirs: \[ \eta = 1-\frac{T_C}{T_H} \] Temperatures must always be in Kelvin.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the thermal efficiency of an ideal Carnot engine operating between two given temperature reservoirs.
Step 2: Key Formula or Approach:
The efficiency (\(\eta\)) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T_{sink}}{T_{source}} \]
Temperatures must be in Kelvin.
Step 3: Detailed Explanation:
1. Identify the temperatures:
Source temperature (\(T_1\)) = \(600 \text{ K}\) (higher temperature).
Sink temperature (\(T_2\)) = \(300 \text{ K}\) (lower temperature).
2. Calculate efficiency:
\[ \eta = 1 - \frac{300}{600} \]
\[ \eta = 1 - 0.5 \]
\[ \eta = 0.5 \]
3. Convert to percentage:
\[ \text{Efficiency %} = \eta \times 100 = 0.5 \times 100 = 50% \]
Step 4: Final Answer:
The efficiency of the Carnot engine is 50%.