# Thermodynamics Power Cycle Energy Balance

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1. Jul 29, 2017

### AGiantGolden49er

1. The problem statement, all variables and given/known data
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)

2. Relevant equations
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)

3. 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.

Last edited: Jul 29, 2017
2. Jul 30, 2017

### CWatters

Not my field but... isn't 100kPa about atmospheric pressure so the temperature of the steam would be...

3. Jul 30, 2017

### Staff: Mentor

What would be the ratio of Qh to Qc if the system were operating reversibly (at maximum theoretical efficiency)? (Qh is the rate of heat addition from the steam reservoir).