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QPage 60: Q14: HC Verma: Concepts of Physics - Volume 2 Laws of Thermodynamics Page 60: Q14 Solution: What should be the condition for the efficiency of a Carnot…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often confuse the condition for 100% efficiency with the source temperature being infinite or the sink being at room temperature; remember that $\eta = 1$ strictly requires the sink temperature $T_2$ to be absolute zero (0 K), which is physically unattainable.

What should be the condition for the efficiency of a Carnot engine to be equal to 1?

Step-by-Step Verified Solution

**Answer:** The efficiency of a Carnot engine equals 1 only if the sink temperature is **0 K**. **Step-by-Step Explanation:** Efficiency of a Carnot engine: η=1−T2T1\eta = 1 - \frac{T_2}{T_1}, where T1T_1 is the source temperature and T2T_2 is the sink temperature. For η=1\eta = 1, we need T2T1=0\frac{T_2}{T_1} = 0, i.e., T2=0T_2 = 0 K (absolute zero). This is unattainable, so η=1\eta = 1 is impossible in practice [citation:8].

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