Reversibility and Carnot cycle

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I have two short questions:

1) Is the Carnot cycle completely reversible?

2) [tex]\Delta S = 0[/tex] for a reversible process, right?
 
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Yes, the Carnot cycle is designed as being reversible.

Yes, it is the Clausius theorem for a reversible cycle. On a particular reversible process, a system can increase o decrease its entropy provided that the surroundings decrease or increase it by the same amount, as the universe entropy will remain constant.