Energy Analysis of Control Volumes at Steady State
4.43 Air expands through a turbine from 10 bar, 900 K to 1 bar, 500 K. The inlet velocity is small compared to the exit velocity of 100 m/s.
The turbine operates at steady state and develops a power output of 3200 kW. Heat transfer between the turbine and its surroundings and
potential energy effects are negligible. Calculate the mass flow rate of air, in kg/s, and the exit area, in m^2.
4.88 As shown in Fig P4.88, electronic components mounted on a flat plate are cooled by convection to the surroundings and by liquid
water circulating through a U-tube bonded to the plate. At steady state, water enters the tube at 20 C and a velocity of 0.4 m/s and exits at
24 C with a negligible change in pressure. The electrical components receive a 0.5 kW of electrical power. The rate of energy transfer by
convection from plate-mounted electronics is estimated to be 0.08 kW. Kinetic and potential energy effects can be ignored. Determine the
tube diameter, in cm.
4.111 As shown in Fig. P4.111, a 300-ft^3 tank contains H2O initially at 30 lbf/in^2 and a quality of 80%. The tank is connected to a large
steam line carrying steam at 200 lbf/in^2, 450 F. Steam flows into the tank through a valve until the tank pressure reaches 100 lbf/in^2 and
the temperature is 400 F, at which time the valve is closed. Determine the amount of mass, in lb, that enters the tank and the heat transfer
between the tank and its surroundings, in Btu.
Refrigeration and Heat Pump Cycle Application
5.63 The refrigerator shown in Fig. P5.63 operates at steady state with a coefficient of performance of 4.5 and a power input of 0.8 kW.
Energy is rejected from the refrigerator to the surroundings at 20 C by heat transfer from metal coils whose average surface temperature is
28 C. Determine (a) the rate energy is rejected, in kW. (b) the lowest theoretical temperature inside the refrigerator, in K. (c) the maximum
theoretical power, in kW, that could be developed by a power cycle operating between the coils and the surroundings. Would you
recommend making use of this opportunity for developing power?
Carnot Cycle Applications
5.75 Two kilograms of water execute a Carnot power cycle. During the isothermal expansion, the water is heated until it is a saturated
vapor from an initial state where the pressure is 40 bar and the quality 15%. The vapor then expands adiabatically to a pressure of 1.5 bar
while doing 491.5 kJ/kg of work. (a) Sketch the cycle on p-v coordinates. (b) Evaluate the heat and work for each process, in kJ. (c)
Evaluate the thermal efficiency.
5.78 One kilogram of air as an ideal gas executes a Carnot power cycle having a thermal efficiency of 50%. The heat transfer to the air
during the isothermal expansion is 50 kJ. At the end of the isothermal expansion, the pressure is 574 kPa and the volume is 0.3 m^3.
Determine (a) the maximum and minimum temperatures for the cycle, in K. (b) the pressure and volume at the beginning of the isothermal
expansion in bar and m^3, respectively. (c) the work and heat transfer for each of the four processes, in kJ. (d) Sketch the cycle on p-v
coordinates.
Analyzing Rankine Cycle
8.9 Water is the working fluid in an ideal Rankine cycle. The pressure and temperature at the turbine inlet are 1600 lbf/in^2 and 1100 F,
respectively, and the condenser pressure is 1 lbf/in^2 The mass flow rate of steam entering the turbine is 1.4 x 10^6 lb/h. The cooling water
experiences a temperature increase from 60 to 80 F, with negligible pressure drop, as it passes through the condenser.
8.19 Reconsider the cycle of Problem 8.9, but include in the analysis that the turbine and pump have isentropic efficiencies of 88%. The
mass flow rate is unchanged. Determine for the modified cycle. (a) the net power developed, in Btu/h. (b) the rate of heat transfer to the
working fluid passing through the steam generator, in Btu/h. (c) the thermal efficiency. (d) the volumetric flow rate of cooling water
entering the condenser in ft^3/min.
9.33 An air-standard dual cycle has a compression ratio of 9. At the beginning of compression, p1 = 100 kPa, T1 = 300 K, and V1 = 14 L.
The heat addition is 22.7 kJ, with one half added at constant volume and one half added at constant pressure. Determine (a) the
temperatures at the end of each heat addition process, in K. (b) the net work of the cycle per unit mass of air, in kJ/kg. (c) the thermal
efficiency. (d) the mean effective pressure, in kPa.
Regeneration, Reheat, and Compression with Intercooling
9.56 Air enters the compressor of a regenerative air-standard Brayton cycle with a volumetric flowr rate of 60 m^3/s at 0.8 bar, 280 K. The
compressor pressure ratio is 20, and the maximum cycle temperature is 2100 K. For the compressor, the isentropic efficiency is 92% and
for the turbine the isentropic efficiency is 95. For a regenerator effectiveness of 85%, determine (a) the net power developed, in MW. (b)
the rate of heat addition in the combustor, in MW. (c) the thermal efficiency of the cycle.
Vapor Regeneration Systems
10.24 A window-mounted air conditioner supplies 19 m^3/min of air at 15 C, 1 bar to a room. Air returns from the room to the evaporator
of the unit at 22 C. The air conditioner operates at steady state on a vapor-compression refrigeration cycle with Refrigerant-22 entering the
compressor at 4 bar, 10 C. Saturated liquid refrigerant at 9 bar leaves the condenser. The compressor has an isentropic efficiency of 70%,
and refrigerant exits the compressor at 9 bar. Determine the compressor power, in kW, the refrigeration capacity, in tons, and the
coefficient of performance.
11.88 Argon gas enters a turbine operating at steady state at 100 bar, 325 K and expands adiabatically to 40 bar, 235 K with no significant
changes in kinetic or potential energy. Determine (a) the work developed, in kJ per kg of argon flowing through the turbine. (b) the amount
of entropy produced, in kJ/K per kg of argon flowing.