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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?
bad_chemist
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  • This question was already answered in another post. – David White Aug 08 '19 at 23:38
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    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. – By Symmetry Aug 08 '19 at 23:43
  • @BySymmetry then why is it valid to apply Carnot's theorem on the turbine? Steam is being "condensed" to water there as well, right? – bad_chemist Aug 09 '19 at 01:02
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    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. – David White Aug 09 '19 at 01:15
  • This is about the way in which “heat” and “work” differ. My answer to a previous question approaches the issue from the other side, but it might be a place to start. – dmckee --- ex-moderator kitten Aug 09 '19 at 02:14
  • Why are you saying that using saturated steam to operate a turbine violates the 2nd law of thermodynamics? And, worse yet, why are you saying that this has to be happening at a constant temperature? It certainly wouldn't occur at constant temperature if the outlet pressure was held lower than the inlet pressure. A turbine in which saturated steam were introduced at the inlet with a pressure drop over the device would operate fine, just as a turbine with the usual superheat, as a nearly adiabatic reversible device. – Chet Miller Aug 09 '19 at 02:17
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    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 ... – dmckee --- ex-moderator kitten Aug 09 '19 at 02:17
  • @ChetMiller I am saying that if a turbine operates with saturated steam and if we want to use the heat of vaporization of steam to do useful work, it would result in a violation of the 2nd law of thermodynamics – bad_chemist Aug 09 '19 at 02:26
  • I understand what you are saying. I just don't see how you can say that. Have you done an actual calculation where saturated steam is introduced into a turbine, and it flows through the turbine adiabatically with a specified pressure drop? – Chet Miller Aug 09 '19 at 02:32
  • If you think that feeding dry saturated steam to a turbine somehow violates the 2nd law, how do you explain the Rankine cycle described in the following reference, where dry saturated steam enters the turbine at 50 bars, and exits the turbine at 0.06 bars as a saturated mixture of steam and liquid water: https://en.wikipedia.org/wiki/Rankine_cycle? – Chet Miller Aug 09 '19 at 02:54
  • @dmckee your comment reminds me of the article by Harvey Leff titled "Thermodynamics Is Easy – I’ve Learned It Many Times", DOI: 10.1119/1.2432080 . I really believe that Truesdell was right, see his quote here https://physics.stackexchange.com/q/396046 – hyportnex Aug 09 '19 at 11:55

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