E234 THERMODYNAMICS Professor Bernard Gallois Exam 3 – April April 10, 2014
1. Cogeneration is often used where a steam supply is needed for industrial process energy. Assume a supply of 5 kg/s steam at 0.5 MPa is needed. Rather than generating this from a pump and boiler, boiler, the setup shown below is used used so the supply is extracted from from the high pressure turbine. turbine. Find the power the turbine turbine now cogenerates cogenerates in this this process. Inlet (1): 20 kg/s 10 MPa, 500oC Exit (2): 5 kg/s process steam, 0.5 MPa, 155oC Exit (3) 15 kg/s, 20 kPa, x = 0.90 Assumptions: steady flow, negligible kinetic energy and potential energy, no heat transfer to the surroundings (adiabatic turbine). Mass balance: mi me
m1 m2 m3 Energy balance: m1h1 WTurbine m2 h2 m3 h3
Using the tables h1 3375.1 kJ/kg h2 2755.3 kJ/kg (need to interpolate) h3 251.4 0.9 x 2357.5 2373.2 k J/ J/kg W 18.13 MW
2. The main waterline into a tall building has a pressure of 600 kPa at 5 m below ground level. A pump brings the pressure up so the water can be delivered at 200 kPa at the top floor 150 m above ground level. Assume a flow rate of 10 kg/s k g/s liquid water at 20oC and neglect any difference in kinetic energy and internal energy u. Find the pump work.
200 kPa 20 oC 12 m/s Pump 600 kPa 20oC 3 m/s
Assume the water is incompressible. The general energy balance at steady flow is given by: 2 2 Vi V e Qin Win mi hi gzi Qout Wout me he gze 2 2
Ignoring heat transfer and noting that there is no work out of the system, the equation reduces to: Win mi hi gzi me he gz e The mass balance is: mi =me Win me he hi g ( z e z i ) he hi ue Peve u i Pv i i
Since the temperature is constant ue ui and the energy balance reduces to Win me Peve Pv i i ) g ( z e z i )
At 20oC, ve = vi = 0.001002 m3/kg, m 10 kg/s Use the fundamental SI units Win 10 (200, 000 600, 000)x 0.001002 9.81x 155
11.2 kW 3. A 2.4-m high 200-m2 house is maintained at 22 C by an air-conditioning system whose COP is 3.2. It is estimated that the kitchen, bath, and other ventilating fans of the house discharge a houseful of conditioned air once every hour. If the average outdoor temperature is 32 C, the density of air is 1.20 kg/m 3, and the unit cost of electricity is $0.10/kWh, the amount of money “vented out” by the fans in 10 hours is
m V 1.2 x 2.4 x 200 / 3600 0.16 kg/s COP W
Q L
mCP T
W W 0.16 x1.005 x10
0.5025 kW 3.2 cost 0.5025x10x0.1=$0.50
4. While on vacation at your grandmother’s in Northern Maine in January, the oil furnace breaks down. As a budding thermodynamicist, you share the following plan with her: we will close all the doors to the kitchen, stay in the kitchen, turn the fridge on and leave the door open. Is this a good plan to stay warm? Be thorough. The only energy that enters the room is electrical energy. The room will heat up, assuming it is well insulated, at a rate of 250 W.
