Consider a system where a Carnot engine is operating between a source and a sink. Which of the following statements about this system is/are NOT correct?
Show Hint
- Reversible cycle \(\Rightarrow \Delta S_{\text{universe}} = 0\).
- Any irreversibility would make \(\Delta S_{\text{universe}}>0\) and reduce efficiency below Carnot.
- This engine is reversible.
- The engine efficiency is independent of the source and sink temperatures.
- This engine has the highest efficiency among all engines that operate between the same source and sink.
- The total entropy of this system increases at the completion of each cycle of the engine.
The Correct Option is B, D
Solution and Explanation
Step 1: Recall the Carnot efficiency.
The efficiency of a Carnot engine is \[ \eta_{\text{Carnot}} = 1 - \frac{T_c}{T_h}, \] which depends only on the absolute temperatures \(T_h\) (source) and \(T_c\) (sink). Hence statement (B), which claims independence from these temperatures, is not correct.
Step 2: Reversibility and optimality.
A Carnot engine is by definition a reversible engine and, for given \(T_h\) and \(T_c\), has the maximum possible efficiency among all engines. Therefore, statements (A) and (C) are correct.
Step 3: Entropy change over a reversible cycle.
For a completely reversible cycle involving the engine and the two reservoirs, the total entropy change of the combined system (engine + reservoirs) over a full cycle is \[ \Delta S_{\text{total}} = 0. \] Thus the total entropy does not increase at the end of each cycle. Hence statement (D) is not correct.
Final Answer: \[ \boxed{\;\; \text{Correct statements: (A) and (C)} \;} \]
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