As shown in Fig. P5.39, a system undergoing a power cycle develops a net power output of 1 MW while receiving energy by heat transfer from steam condensing from saturated vapor to saturated liquid at a pressure of 100 kPa. Energy is discharged from the cycle by heat transfer to a nearby lake at 17°C. These are the only significant heat transfers. Kinetic and potential energy effects can be ignored. For operation at steady state, determine the minimum theoretical steam mass flow rate, in kg/s, required by any such cycle.
Fig. 5.39: https://gyazo.com/49a3ca702a5fa239633f8f054618345e
(Can't get it to embed)
η = Wcycle / QH = 1 - TC / TH
Wcycle = QH - QC
mass flow: dmcv / dt = ∑ mi - ∑ me
energy balance: dEcv / dt = Q - W + ∑ mi(hi + Vi2 / 2 + gzi)- ∑ me(he + Ve2 / 2 + gze)
The Attempt at a Solution
Knowing that the system operates at steady state, I know that the entry mass flow and exit mass flow are the same. I also know that since kinetic energy and potential energy can be ignored, the energy balance equation simplifies to:
0 = Q - W + ∑ mi(hi)- ∑ me(he) =>
W = Q + m(hi - he)
Knowing that the initial and final states are at saturated vapor and saturated liquid, respectively, using the tables in the back of the book, I found the specific enthalpy values to be:
h1 = 2675.5 kJ/kg
h2 = 417.46 kJ/kg
I know that I can use the thermal efficiency relation to find the QH value, but I don't know how exactly to find the thermal efficiency since there's no listed TH value, unless I'm missing something in the problem statement. I feel that the energy balance equation will be cake once the heat transfer value is found, but I just can't figure out how to get it. If anyone could steer me in the right direction, that would be appreciated.
Edit: The temperature of the lake is 17°C, not 178C. Copy-and-paste didn't recognize the degree symbol.