Homework #8 MEMS 0051 – Introduction to Thermodynamics solved

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Problem #1
Steam enters a turbine through a pipe with a diameter of 0.2 [m]. The steam enters with a velocity of 100
[m/s], a pressure of 14,000 [kPa] and a temperature of 600 ◦C. The steam is exhausted through a pipe with
a diameter of 0.8 [m], a pressure of 500 [kPa] and a temperature of 180 ◦C. Determine:
a) the exit velocity of the steam;
b) the mass flow rate of the steam.
Problem #2
An open feedwater heater (OFWH) accepts liquid water at 1,000 [kPa] and a temperature of 50 ◦C. The
OFWH also accepts water with a mass flow rate per that of inlet one, i.e. ˙m2/ ˙m1=0.22. Saturated liquid
water exits the OFWH. Determine:
a) the temperature of the second incoming stream, if superheated;
b) the quality of the second incoming stream, if saturated.
Problem #3
Steam enters a nozzle operating at a pressure of 30 [bar] and a temperature of 320 ◦C with negligible velocity.
The steam exits the nozzle at a pressure of 15 [bar] and a velocity of 10 [m/s]. The mass flow rate is 2.5
[kg/s]. Assume the nozzle is well insulated.
a) Determine the exit temperature of the steam.
Problem #4
Air expands through a turbine with a mass flow rate of 10 [kg/s] from a pressure of 5 [bar] to 1 [bar] The
temperature of the air at the inlet is 900 [K] where it is 600 [K] at the outlet. The inlet velocity is negligible,
but the exit velocity is 100 [m/s]. All heat transfer and potential energy changes can be neglected.
a) Determine the power output of the turbine in [kW].
b) Determine the exit cross-sectional flow area in [m2
].
Problem #5
An air-conditioner’s cooling coil is a heat exchanger that extracts heat from air and it is picked up by the
working fluid, R-134A (Table B.5, page 180). Air is passed over the heat exchanger coils. Air enters the
heat exchanger with a volumetric flow rate of 40 [m3/min], a temperature of 40 ◦C and a pressure of 1 [bar]
and exits at a temperature of 20 ◦C. The R-134A enters the heat exchanger with a quality of 40% at a
temperature of 10 ◦C and exits as a saturated vapor at the same temperature.
a) Determine the mass flow rate of the R-134A.
b) Determine the rate of energy transfer, in [kJ/min], form the air to the refrigerant.
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Problem #6
A pump delivers water at a volumetric flow rate of 0.05 [m3
] through an 18 [cm] diameter pipe located 100
[m] above the pump inlet, which has a diameter of 15 [cm]. The pressure at the inlet and exit of the pump
is equal to 1 [bar], and the temperature can be assumed constant at 20 ◦C.
a) Determine the power input into the pump in [kW].
Problem #7
A tank contains 2 [ft3
] of air with an initial pressure of 50 [psi] and an initial temperature of 70 ◦F. The
tank is punctured and air flows out at a constant mass flow rate of 0.01 [lbm/s]. Using the ideal gas law,
determine:
a) the rate of change of mass within the tank the moment the leak occurs;
b) the mass of air in the tank as a function of time (plot).
Problem #8
A very well insulated chamber with volume of 1 [m3
] contains air initially at 101 [kPa] and 37.8 ◦C. Supply
and discharge lines are connected to the chamber. The supply air is at 200 [kPa] and 93.3 ◦C. The discharge
line is connected to atmosphere. At time t=0, the valves are simultaneously opened, allowing air to flow at
a constant rate of 1 [kg/min] through both lines. The air within the chamber can be assumed well mixed,
i.e. a uniform temperature and pressure at each time step. Determine:
a) the temperature, in ◦C, as a function of time;
b) the pressure, in [kPa], as a function of time.
Problem #9
A Rankine cycle consists of a boiler, turbine, condenser and pump. Steam enters the turbine at 8.0 [MPa]
and 480 ◦C. Saturated liquid exits the condenser at a pressure of 8.0 [kPa]. The net power output of the
cycle is 100 [MW]. Treating each device as a steady-state device, however, linked in series (i.e. constant mass
flow), determine:
a) the mass flow rate of the steam, ˙msteam;
b) the heat input through the boiler, Q˙
h in [MW];
c) the heat output through the condenser, Q˙
c in [MW];
d) the thermal efficiency, and compare to the Carnot efficiency.
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