Carnot Engine

Referring to NCERT Class 11, Chapter 12 (Thermodynamics), the Carnot engine is the ideal reversible engine and is the most efficient engine that can operate between two given temperatures; no real engine working between the same reservoirs can do better. Its efficiency is remarkable in depending only on the absolute temperatures of the source and sink and not on the working substance: $\eta =1-\frac{T_C}{T_H}$, with both temperatures measured in kelvin. Substituting the source temperature $T_H=600$ K and the sink temperature $T_C=300$ K gives $\eta =1-\frac{300}{600}=1-0.5=0.5$, that is 50 percent. The option 75 percent is wrong because it would require a temperature ratio of 1/4, not the 1/2 given here. The option 25 percent is wrong because it inverts or mishandles the ratio, mistakenly taking $T_C/T_H$ itself as the efficiency. The option 100 percent is impossible since it would require the sink to be at absolute zero, which the Third Law of Thermodynamics forbids. A plausibility check confirms the result: efficiency grows as the temperature gap widens relative to the source; here the sink is exactly half the source temperature, so discarding half the input and retaining half as available work (50 percent) is internally consistent, and the value lies safely between 0 and 1.