Question

If the temperature of the source in a Carnot engine is increased while the sink temperature remains constant, the efficiency will:

• A. Increase
• B. Decrease
• C. Remain the same
• D. Become zero

Hint:

Important Points about Carnot Engine: Efficiency depends only on reservoir temperatures. Higher source temperature $\Rightarrow$ higher efficiency. Lower sink temperature $\Rightarrow$ higher efficiency.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The efficiency of a Carnot engine is a theoretical limit on the maximum work that can be extracted from a heat engine operating between two temperatures. It depends only on the absolute temperatures of the source and the sink.
Step 2: Key Formula or Approach:
The efficiency (\(\eta\)) is given by: \[ \eta = 1 - \frac{T_{sink}}{T_{source}} \]
Step 3: Detailed Explanation:
1. Let the original temperatures be \(T_1\) (source) and \(T_2\) (sink).
2. \(\eta = 1 - \frac{T_2}{T_1}\).
3. If \(T_1\) (source) increases, the fraction \(\frac{T_2}{T_1}\) becomes smaller because the denominator is larger.
4. When you subtract a smaller number from 1, the result (\(\eta\)) becomes larger.
5. Therefore, increasing the source temperature (or decreasing the sink temperature) makes the engine more efficient.
Step 4: Final Answer
The efficiency will increase.