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Suppose you have saturated steam entering a turbine. If the turbine condenses the saturated steam to saturated liquid water and uses the heat of vaporization to do useful work, we say that this process violates Carnot's efficiency or the second law of thermodynamics. This is because we are undergoing a phase change at constant temperature. Therefore, $T_h=T_c \implies \eta _{Carnot} = 1-\frac{T_h}{T_c} = 0$.

However, the same process can happen in a condenser and we say that the condenser simply expels the rejected heat.

I have two questions:

  1. Can a turbine thoeretically extract more work from steam coming at $T_h$ by utilizing the heat of vaporization and more by discharging the outlet stream at a lower temperature $T_c < T_h$? I understand that water formation inside the turbine is extremely detrimental to it, but can a turbine possibly do this?
  2. Why does a condenser not violate Carnot's law of maximum efficiency?
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  • $\begingroup$ This question was already answered in another post. $\endgroup$
    – David White
    Commented Aug 8, 2019 at 23:38
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    $\begingroup$ The process you are describing is not a cycle, so Carnot's theorem does not apply. After condensing you need to vaporize the water again so it can restart the process. If this is done at the same temperature as you condensed it, you will be unable to extract any net work. $\endgroup$
    – By Symmetry
    Commented Aug 8, 2019 at 23:43
  • $\begingroup$ @BySymmetry then why is it valid to apply Carnot's theorem on the turbine? Steam is being "condensed" to water there as well, right? $\endgroup$
    – bad_chemist
    Commented Aug 9, 2019 at 1:02
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    $\begingroup$ Steam turbines extract PV work from steam via the differential pressure across the turbine. They do NOT extract work solely from the heat that the steam contains. $\endgroup$
    – David White
    Commented Aug 9, 2019 at 1:15
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    $\begingroup$ That said, I found it nearly impossible to reason about individual points in the historical approach to thermo until I had a pretty good grasp of the whole sweep of the subject. And for me that didn’t happen until the third time through the subject. Donations for a gilded dunce cap can be made to ... $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Aug 9, 2019 at 2:17

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