# End expansion point on overheated Rankine cycle

In an overheated Rankine cycle, the end point of the adiabatic expansion could end inside the dual-phase bell, or on the right.

In the first case, the end expansion point falls of course on the isothermobaric curve at the saturation pressure of the work fluid at the lower temperature Tlow of the cycle (usually room temperature), where it will be condensed into the condenser, as water has already started to appear.

But in the second case, the expansion stops at a temperature Tx greater than Tlow seen in the previous case, but at the very same pressure. Why? I mean, how the work fluid knows it has to stop at that pressure? Why it does not expand until its temperature reaches Tlow, at a lower pressure - from where the fluid should be isothermally compressed until it reaches the upper limit curve , where it can start to condense to get back to start conditions?

Sorry if the question may be stupid, but I need to study, after many years far away from thermodynamics, the Rankine cycle. Please be patient.

• Are you asking what determines the exit pressure from the turbine? – Chet Miller Apr 26 '18 at 1:33
• Yes, especially for overheated Rankine – Nillus Apr 26 '18 at 6:52
• The temperatures and pressures at different points through the Rankine cycle are controlled by the rate of heat addition in the heater and the rate of heat removal in the condenser. Plus, once the gas exits the turbine, it is no longer doing any work so its pressure stops decreasing and remains relatively constant through the condenser. Why don't you run a sample calculation to determine the temperatures and pressures at different locations through the cycle, and the amount of work delivered by the compressor. – Chet Miller Apr 26 '18 at 10:44

Normally condensers are designed to operate at a pressure lower than the atmospheric pressure and this is the minimum pressure to which you can expand the steam in the turbine. This is done beacuse the saturation temperature corresponding to atmospheric pressure is $100^\circ$C and this is much more than the atmospheric temperature which acts as sink for the condenser. A temperature difference of $10^\circ$C to $15^\circ$C is enough for effective heat transfer from condenser to atomsphere.So if the atmospheric temperature is $20^\circ$C we can extract work from turbine untill the steam temperature reaches almost $30^\circ$C. To achieve this, we need to maintain the condenser at a pressure lower than the atmospheric pressure.
Superheating /overheating will not increase the pressure limits of the expansion process as pressure limits are decided by condenser and pump. Hence as we increase superheating the isentropic expansion line in the TS diagram will move towards right and it will meet the condensor pressure line at a higher temperature .This is not a desired result. Hence we mainly incorporate superheating in rankine cycle to increase the steam quality at output so that the turbine blades are less prone to corrosion. Otherwise condenser pressure needs to be further reduced so that further expansion in turbine can be achieved upto $30^\circ$C. But maintaining high vaccum inside condenser itself is a difficult task!