Question

In a carnot engine, the ratio of the heat rejected to the sink to the heat absorbed from the source is 1 : 4. If this ratio is changed to 1: 2, the change in engine efficiency is

• A. 75%
• B. 50%
• C. 25%
• D. 20%
• E. 80\%

Hint:

Carnot efficiency only depends on the temperatures or the heat ratios. Lower heat rejection always implies higher efficiency. If rejection ratio increases, efficiency must drop.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Efficiency (\(\eta\)) of a Carnot engine is the ratio of work done to the heat absorbed.
It can be expressed in terms of heat absorbed (\(Q_1\)) and heat rejected (\(Q_2\)).

Step 2: Key Formula or Approach:
Efficiency \(\eta = 1 - \frac{Q_2}{Q_1}\), where \(Q_1\) is heat absorbed and \(Q_2\) is heat rejected.

Step 3: Detailed Explanation:
1. Initially, the ratio \(Q_2/Q_1 = 1/4\).
\[ \eta_1 = 1 - \frac{1}{4} = \frac{3}{4} = 0.75 = 75\% \]
2. Finally, the ratio is changed to \(Q_2/Q_1 = 1/2\).
\[ \eta_2 = 1 - \frac{1}{2} = \frac{1}{2} = 0.50 = 50\% \]
3. The change in efficiency:
\[ \Delta \eta = |\eta_1 - \eta_2| = |75\% - 50\%| = 25\% \]

Step 4: Final Answer:
The change in engine efficiency is 25%.