Question

Urgent

An industrial process discharges 5,700 m3/min of gaseous products at 200°C, 100 kPa. The figure below shows a proposed system for utilizing the combustion products and its steady state conditions. Heat transfer from the outer surface of the steam generator (heat exchanger) and turbine can be ignored, as can the changes in kinetic and potential energies of the streams. There is no pressure drop through the heat exchanger. The combustion product can be modeled as air as an ideal gas Determine a) b) c) The turbine inlet temperature, T4; the power developed by the turbine; and the rates of entropy generation in the heat exchanger and turbine, each in kW/K Combustion products in P 100 kPa T1-480K (AV5700 m3/min Turbine Power out 4 P4 300 kPa Combustion products out P2 100 kPa 2-400 K Steam enerator 3l Water in P3 = 300 kPa T3 = 40°C m3 120 kg/min Water out P5 = 5 kPa X5 = 97%

Answer 1

State 1

By ideal gas equation

P1 V1 = ma R T1

100 * 5700/60 = ma * 0.287 * 480

ma = 68.9605 kg/s

State 2

400 K

State 3

300 kPa, 400C

h3 = 167.79 kJ/kg --- from compressed water table

s3 = 0.57229 kJ/kg-K --- from compressed water table

Heat lost by air = Heat gained by water

ma Cp (T1 - T2) = mw (h4 - h3)

68.9605 * 1.005 (480 - 400) = 2 (h4 - 167.79)

h4 = 2940.00‬ kJ/kg

State 4

300 kPa, h4 = 2940.00‬ kJ/kg

T4 = 2360C --- from superheated vapor table

s4 = 7.463 kJ/kg-K --- from superheated vapor table

State 5

5 kPa, x = 97%

hf = 137.75 kJ/kg , hg = 2560.7 kJ/kg --- from saturated pressure table

h5 = hf + x5 (hg - hf)

h5 = 137.75 + 0.97 (2560.7 - 137.75)

h5 = 2488.01 kJ/kg

sf = 0.47620 kJ/kg-K , sg = 8.3938 kJ/kg-K --- from saturated pressure table

s5 = sf + x5 (sg - sf)

s5 = 0.47620 + 0.97 (8.3938 - 0.47620)

s5 = 8.156272‬ kJ/kg

Wturb = mw (h4 - h5)

Wturb = 2 (2940.00‬ - 2488.01)

Wturb = 903.98 kW

SHX = S1-2 + S3-4

SHX = ma Cp ln (T2 / T1) + mw (s4 - s3)

SHX = 68.9605 * 1.005 ln (400 / 480) + 2 (7.463 - 0.57229)

SHX = 1.145569 kW/K

Sturbine = S4-5

Sturbine = mw (s5 - s4)  

Sturbine = 2 (8.156272‬ - 7.463)

Sturbine = 1.386544‬ kW/K

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