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# Which of the following Carnot's engines have maximum efficiency?A) Working between 300 K and 0 KB) Working between 800 K and 400 KC) Working between 100 K and 10 KD) Working between 300 K and 200 K

Last updated date: 09th Sep 2024
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Hint: The efficiency of a Carnot engine depends on the temperature of the source and the sink of the engine. The source has a higher temperature and provides heat to the engine while the sink has a lower temperature and removes heat from the system.

Formula used: In this solution, we will use the following formula:
Efficiency of a Carnot engine: $\eta = 1 - \dfrac{{{T_1}}}{{{T_2}}}$ where ${T_1}$ is the source temperature and ${T_2}$ is the sink temperature.

For option (A), $\eta = 1 - \dfrac{0}{{300}} = 1$
For option (B), $\eta = 1 - \dfrac{{400}}{{800}} = 0.5$
For option (C), $\eta = 1 - \dfrac{{10}}{{100}} = 0.9$
For option (D), $\eta = 1 - \dfrac{{200}}{{300}} = 0.33$
The temperature in option (A) is a theoretical one since no object can have 0 Kelvin in this universe. Also, the derived efficiency is also theoretical. In reality, there will always be energy losses in the system. So, the maximum efficiency of a Carnot engine can only reach about $0.7$ practically. The Carnot engine is the most efficient engine in converting heat energy to work done in a system but no practical Carnot engine can be $100\%$ efficient in reality.