Understanding Closed Feedwater Heaters and Regeneration in the Rankine Cycle

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I have a question on the rankine cycle with a closed feedwater heater. My thermo book says that in an ideal closed feedwater heater, the feedwater is heated to the exit temperature of the extracted steam. I don't really understand this. I know the bleed steam from the turbine is cooled to a saturated liquid after it heats the feedwater but I don't what limits the two exit temperatures to be equal.

Also I have a general questions about regeneration. I was looking at a regenerator in which exhaust gas from a turbine is used to preheat the gas before it enters the combustion chamber. How is it possible for the exhaust gas leaving the regenerator(cooled) be at a lower temperature than the gas right before the combustion chamber(heated). I would think that if the exhaust gas were at a lower temperature the heat transfer would be reversed.

Thanks for any help
 
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"in an ideal closed feedwater heater, the feedwater is heated to the exit temperature of the extracted steam"
Well its pretty much easy. All you are doing in a feedwater heating system is reducing the work required for the compressor(a few more things also, but this is the priority now). When the compressor compresses, the feedwater is heated to some temperature depending upon the pressure jump, now a calculated amount of steam is allowed to pass through the heater(either contact or non contact type exchanger). this amount is calculated by assuming the heat released by change of phase of steam is equal to the heat required to raise the temperature to the phase change temperature. Keep in mind that phase change is an isothermal process,=> temperature remains constant. Ofcourse now as the system is assumed ideal and heat transfer perfect, feedwater temp is same as that of extracted steam. Or it can be even higher, if the steam is bleeded in superheated region.