Question

The efficiency of a Carnot engine is \(50\%\) and the temperature of the sink is \(500\,\text{K}\). Keeping the source temperature constant, the required sink temperature to raise the efficiency of the engine to \(60\%\) is

• A. \(100\,\text{K}\)
• B. \(400\,\text{K}\)
• C. \(500\,\text{K}\)
• D. \(600\,\text{K}\) \bigskip

Hint:

For a Carnot engine, \[ \eta=1-\frac{T_2}{T_1}. \] To increase efficiency while keeping the source temperature fixed, the sink temperature must be decreased.

Answer 1

The Correct Option is B

Concept: Carnot efficiency \(\eta = 1 - T_2/T_1\). Initially \(0.5 = 1 - 500/T_1 \Rightarrow T_1 = 1000\) K. For 60%: \(0.6 = 1 - T_2'/1000 \Rightarrow T_2' = 400\) K.

Step 1: Write the final answer. \(\boxed{400\,\text{K}}\)