Conduct a first law analysis of the boiler and the turbine in for the cycle in Exercise 2.25. Written for a time dependent process, i.e.
Here all terms are rate terms. Q˙ and W˙s are rate of heat transfer and rate at which work is done. For steady state processes dE /dt = 0 because the total energy of the system does not change in time. The terms dni/dt are mass flow rates at the ports with flow in positive.
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You are impressed that the most efficient cycle must transfer heat isothermally and that the other legs of the cycle must be isentropic. The cycle plotted on (S,T) coordinates is a rectangle. You know that the isentropic assumption may be made when a fluid flows rapidly, because then the heat transfer per mol is small. Turbines do this very well. So you can use a turbine to obtain work isentropically. You also know that water boils and condenses at constant temperatures if the pressures are held constant. In Fig. 2.9 we have plotted the idea in (S,T) coordinates for water. The saturation line and the phases of water are indicated.
The Carnot cycle is a→b→c→d. The leg b→c is the turbine, and you propose to pump the partially condensed liquid from d→a to enter the boiler. The difficulty becomes clear after some thought. So you elect to heat the steam to a higher temperature before entrance to the turbine and you allow the condensation to run to completion. The result is the cycle a→b→e→f→c→d→g→h. The small vertical leg g→h is the liquid pump, which is also isentropic.
(a) Explain the problems that led to super heating and full condensation.
(b) In which legs are work done and is this by or on the system?
(c) Draw the cycle on a sheet of paper and indicate heat into the cycle and heat exhausted.
(d) What represents the work done?
(e) Where are boiling and condensation? This cycle is actually the Rankine cycle and forms the basis of power production.