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According to 2nd law of thermodynamics, it is not possible to convert heat 100% into work.

Well, investigating about the Carnot Cycle, I have found out that in the first step, the process is to heat a gas without rising its temperature, this is, converting all the heat into work. Isn't this a violation of the 2nd law?

I clearly don't understand something about the law or about the Carnot Cycle. I would like to know where I'm failing in my understandig. Thank you.

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    $\begingroup$ the Carnot cycle is a CYCLE, and its efficiency being always less than 1 refers to the cycle not to any one of its legs. $\endgroup$
    – hyportnex
    Commented Jun 6, 2016 at 18:52
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    $\begingroup$ Yes, but if we just took the first step, ignoring the rest of the cycle, wouldn't we be violating the 2nd law? Or the 2nd law just applies to closed cycles? $\endgroup$
    – Diego López
    Commented Jun 6, 2016 at 18:56
  • $\begingroup$ that in a Carnot cycle the efficiency is <1 is one possible formulation of the 2nd law. $\endgroup$
    – hyportnex
    Commented Jun 6, 2016 at 20:00

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It is possible to convert heat 100% into work provided that something else happens to your heat machine (i.e. the heat-to-work conversion system). In your case, the gas has expanded, so the state of the heat machine is not the same as in the beginning.

The 2nd law of thermodynamics states that it is not possible to convert heat 100% into work AND have the heat machine in a state that is identical to its initial state.

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The second law of thermodynamics states that complete conversion of heat into work is not possible in a cycle. Of course the first step in Carnot cycle is the isothermal expansion where heat absorbed is converted into work, but the final state after isothermal expansion is not as the initial one or it is not cyclic. But when the Carnot cycle is completed you will find that the part of heat absorbed is rejected and remaining part is coknverted into work which is clearly what second law states.

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Carnot cycle postulated that the four steps are reversible. So, according to the 2nd law, the change of entropy would be zero. Even though, there still an increase in entropy due to the increase of the gas volume upon its expansion. This is the reason that the cycle efficiency never be 1 even in the reversible conditions.

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The Carnot cycle contains two isotherms and two adiabats (look at the PV diagram if you haven't seen it). The isothermal compressions and expansions convert all of the heat to work with no change in energy. While the adibatic compressions and expansions lose no heat and the change in internal energy is directly proportional to the work done on the gas.

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