Question

11) An adiabatic compressor is to be powered by a direct-coupled adiabatic turbine that is also driving a generator. Steam enters the turbine at 10 MPa and 500 °C at a rate of 15 kgs and exits at 20 kPa. The turbine isentropic efficiency is 85% Air enters the compressor at 98 kPa and 230C at a rate of 10 kg/s, and exits the compressor at 1.2 MPa. The compressor efficiency is 75 %. Determine: a) the power requirement of the compressor b) the rate of electrical power generation, if the mechanical efficiency of the electric generator is 88%, the rate of entropy generation for entire process. c)

Answer 1

p_1 = 98k pa T_1 = 296 k M_1 = 10 kg/s p_2 = 1.2 M pa T_2 = 620 k p_4 = 20 k pa x = 0.75 p_3 = 10 M pa T_3 = 500 degree c M_3 = 15 kg/s T_1 = 296 k Enthalpy h_1 = 295.17 kj/kg s^0_1 = 1.68515 kj/kg k T_2 = 620 k h_2 = 628.07 kj/kg s^0_2 = 2.44356 kj/kg k p_3 = 10 M pa, T_3 = 500 degree c = 773 k tildeequal 800k doublerightarrow h_3 = 822.14 kj/kg, s_3 = 2.718 kj/kg k p_4 = 20 k pa Enthalpy of saturated liquid, h_f = 383.62 Enthalpy of evaporceded liquid h_sg = 4784.2 Enthalpy at state 4, h_4 = h_s + x h_fg \r\n h_4 = 3971.77 kh/kg s_f = 1.2984, s_fg = 14.9992 Endropy at state 4 = s_4 = s_f + x s_fg = 12.5478 kj/kg k E_in - E_out = delta E_system = 0(s deady)