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Pressure and power for adiabatic compressor

a) Air flowing at 1 m3/s enters an adiabatic compressor at 20°C and 1 bar. It exits at 200°C. The isentropic efficiency of the compressor is 80%. Calculate the exit pressure and the power required.

b) Steam enters a turbine at 10 MPa and 500°C and leaves at 100 kPa. The isentropic efficiency of the turbine is 85%. Calculate the exit temperature and the work generated per kg of steam flowing through.

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(a) The isentropic efficiency = (Texit,s – Tin)/(Texit,a – Tin) ... subscript s refers to isentropic and a refers to actual temperatures.

0.8 = (Texit,s – 20)/(200 – 20)

Texit, s = 164 oC

Hence, Pexit = (Tin/Texit,s)γ/(1-γ)Pin = (283/437)1/4/(1-1.4) (1 bar) = 4.58 bar

To find the power required,

energy or enthalpy actually changed = Cp (T2-T1) = 1(200-20) = 180 kJ/kg

mass flow rate of air = density x volumetric flow rate.

= 0.98 x 1 = 0.98 kg/s

Power required = mass flow rate x enthapy change per unit mass
                       = 0.98 x 180 = 176.4 kW

(b) Texit,s = (Pexit/Pin)(γ-1)/γTin = (100/10000)(1.4-1)/1.4(500)  = 134.13 oC

Isentropic efficiency for turbine = (Texit – Tin)/(Texit,s – Tin)
                                              = 0.85

Texit = 0.85(134.12 – 500) + 500 = 189 oC

Work generated = -Cp(Texit – Tin) = 2.28(500 – 189) =   709.8 kJ/kg

Answers, exit temperature is 189 oC and work generated is 709 kJ per kg of steam.

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