2. (25 points) Superheated steam at 410°C and 400 kPa flowing at 3,000 kg/s ente

Question

2. (25 points) Superheated steam at 410°C and 400 kPa flowing at 3,000 kg/s enters a turbine to produce work. a. Assume the turbine is adiabatic (no heat loss) and that the steam leaves as saturated liquid at 400 kPa. Find the outlet temperature and work produced. and the work produced is 7,000,000 kJ/s. Assume the inlet feed stays the same. The b. Now consider the case where the turbine is not adiabatic (heat loss of 20,000 k.J/s) outlet water leaves at 350 kPa in this case. What is the outlet enthalpy, temperature, and state (saturated liquid, saturated vapor, etc.)?

Explanation / Answer

a) Inlet conditions: Feed = 3000 Kg/s: Temperature= 410°C, Pressure=400 Kpa

Enthalpy of feed= 3292.9 KJ/kg(from steam table)

Outlet conditions: Saturated water at 400 Kpa: Outlet temperature= 143.61 °C (from steam table)

Enthalpy= 604.65 KJ/Kg

Work output= (3292.9-604.65)*3000=8064750 KJ/s

b) Outlet enthalpy = Inlet enthapy*flow - Heat Loss-Work produced

= 3292.9*3000-20000-7000000 = 2858700 KJ/s = 2858700/3000 =952.9 KJ/Kg

Outlet Temperature= 138.86°C(from steam table)

Let x be the vapour fraction of water in the outlet stream

Then,

952.9= (1-x)*584.26+x*2732 [ Enthalpy of saturated liquid at 350KPa= 584.26 KJ/Kg ; Enthalpy of saturated Vapour at 350KPa = 2732 KJ/Kg]

x=0.172 That means a mixture of vapour and Liquid.

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