Question

An ideal Carnot engine has an efficiency of 40 %. The ratio of the temperature of the sink to that of the source is

• A. 0.4
• B. 0.6
• C. 0.5
• D. 0.2
• E. 0.3

Hint:

For a Carnot engine, the efficiency depends on the ratio of the temperatures of the sink and the source. A higher ratio means a less efficient engine.

Answer 1

The Correct Option is B

The efficiency of a Carnot engine is given by the formula: \[ \eta = 1 - \frac{T_{\text{sink}}}{T_{\text{source}}} \] Where: - \(\eta\) is the efficiency, - \(T_{\text{sink}}\) is the temperature of the sink (cold reservoir), - \(T_{\text{source}}\) is the temperature of the source (hot reservoir). We are given that the efficiency \(\eta = 0.40\), so: \[ 0.40 = 1 - \frac{T_{\text{sink}}}{T_{\text{source}}} \] Solving for the ratio \(\frac{T_{\text{sink}}}{T_{\text{source}}}\): \[ \frac{T_{\text{sink}}}{T_{\text{source}}} = 1 - 0.40 = 0.60 \] Thus, the correct answer is (B) 0.6.