a company has decided to build a new steam (working fluid ; water) power cycle.

Question

a company has decided to build a new steam (working fluid ; water) power cycle. The boundary tempertures are 800 degrees celcius and 150 degrees celcius, respectively for the hot and cold boundaries of the cycle where heat is added and rejected. The turbine has an isentropic efficiency of 72%, inlet water conditions of 16.0 Mpa and 720 degree celcius, and an exit pressure of 2.0Mpa. Although the turbine is not ideal you may asume it to be prefectly insulated.

(a) Find the acutal work output per unit mass from the turbine.

(b)Find the maximum possible work per unit mass output from the turbine.

(c) If the cycle is used only to produce power, find the second law efficiency of the cycle. The cycle has the following conditions:(1) the heat rejection from the condenser is 40% of the actual turbine output work, and (2) the pump work input is 15% of the actual turbine output work.

(d) The unit costs for heat at the high and low temperature boundaries are equal. The capitol cost for all equipment and maintenance is $2,500 per kg of water.If the unit cost of the work produced by the tubine and work input for the pump is $300 per Kj/Kg, find the unit cost for the heat transfer from the high temeperature reservior.

Explanation / Answer

FOR TURBINE INLET

a) From the steam tables

at P = 16 MPa

Tsat = 347.5 deg

Given T = 720 deg

T > Tsat ,Therefore the state is superheated

hi = 3885 kJ/kg

TURBINE OUTLET

P = 2 MPa

he = 2800 kJ/kg

First law for CV for Turbine

q + hi = w + he

Here q = 0 (insulated)

w = hi - he = 1085 kJ/kg

Since The efficiency of Turbine is 72 %

w(actual ) = w*efficiency = 0.72*1085 = 781.2 kJ/kg

b) Max Possible work = w = 1085 kJ/kg (for 100% efficiency of turbine)

c)

qout = 0.4*w(actual) = 0.4*781.2 = 312.48 kJ/kg

w(input) = 0.15*w(actual) = 117.18 kJ/kg

Net Work = W(actual) - W(input) = 781.2 - 117.18 = 664.02

qin = w(actual) + qout = 1093.68

Efficiency = net work/qin = 60.71%

d)

Cost for 1 unit = 300/(win+wactual) = 0.334 dollors

For qin

Total cost = 0.334*1093.68 = 365.22 dollors/kJ/kg

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