Modern Engineering Thermodynamics

Problems 199
Problems (* indicates problems in SI units)
1. Determine an expression for the time rate of change of the total
internal energy of a submarine that is
a. Not insulated.
b. Being propelled by its propeller shaft.
c. Taking on ballast water at only one opening in the
submarine.
d. Is diving and accelerating.
2. Write the complete energy rate balance (ERB) for an automobile
accelerating up a hill and provide a physical interpretation for
each term in the balance.
3. A new perfume is produced in the rigid, insulated reactor vessel
shown in Figure 6.22. Determine the electrical power required
to maintain the process in a steady state, steady flow condition.
Neglect any changes in kinetic or potential energy.
Chemical A
m A = 0.100 lbm/h
h A = 100. Btu/lbm
Chemical B
h B = 50.0 Btu/lbm
FIGURE 6.22
Problem 3.
Electrical
heater
W elect = ?
Reactor product
m p = 2.00 lbm/h
h p = 400. Btu/lbm
Rigid reactor
vessel
4.* Determine the adiabatic change in temperature of a river that
aergonically drops 1.00 m over a waterfall without a change in
velocity. The specific heat of the river water is 4.20 kJ/(kg · K).
5. A small hydroelectric power plant discharges 200. ft 3 /s of
water. If the elevation difference ðZ in − Z out Þ between the inlet
and outlet is 15.0 ft and the temperature difference ðT in − T out Þ
is −0.0100°F, determine the mass flow energy transport
rate. Assume the inlet and outlet velocities are identical:
c = 1.00 Btu/(lbm · R) and ρ =62.4lbm/ft 3 .
6. Air flows aergonically at a constant rate of 8.00 lbm/min down
a horizontal duct so that its enthalpy remains constant. As the
air flows down the duct, its velocity increases from 500. to
650. ft/s. Find the heat transfer rate and indicate whether it is
to or from the system. Assume steady state operation.
7. A steady state air compressor takes in air at atmospheric pressure
and discharges it at 100. psia. The inlet enthalpy is 120. Btu/lbm
and the exit enthalpy is 176 Btu/lbm. Heat is transferred out of
the compressor to cooling water at the rate of 1600. Btu/min. If
the air flow rate through the compressor is 10.0 lbm/min, what
horsepower must be supplied to the compressor? Neglect the
kinetic and potential energies of the inlet and outlet flow
streams.
8. Refrigerant-134a enters a constant area tube at 100.°F witha
quality of 75.0%. Heat is transferred in a steady flow aergonic
process until the R-134a leaves as a saturated liquid at exactly
0°F. Determine the heat transfer per lbm of R-134a flowing.
Neglect any changes in kinetic and potential energies. Assume
steady state operation.
9. An architect designed a 2.00 mile-high skyscraper. Steam is used
for heating and is to be supplied to the top floor via a vertical
pipe. The steam enters the pipe at the bottom as dry saturated
vapor at 30.0 psia. At the top floor, the pressure is to be 16.0
psia, and the heat transfer from the steam as it flows up the
pipe is to be 50.0 Btu/lbm. What is the quality of the steam at
the top floor?
10.* How many watts of power could be recovered by decelerating
0.500 kg/s of air in a ventilating system from 10.0 m/s to
0.100 m/s before discharging it to the atmosphere?
11. Water initially at 300. psia and 500.°F is expanded isothermally
and adiabatically to 14.7 psia in a horizontal steady flow
process. In the absence of work modes, determine the change in
kinetic energy per pound of water.
12. Refrigerant-134a expands in a steady flow diffuser from 300.
psia, 180.°F to 35.0 psia in an isothermal process. During this
process the heat transfer from the R-134a is 3.10 Btu/lbm.
Assuming a negligible exit velocity, determine the inlet velocity
to the diffuser.
13. A steam whistle is devised by attaching a simple converging nozzle
to a steam line. At the inlet to the whistle, the pressure is 60.0 psia,
the temperature is 600.°F, and the velocity is 10.0 ft/s. The steam
expands and accelerates horizontally to the outlet, where the
pressure and temperature are 14.7 psia and 500.°F. Determine the
steam velocity at the whistle outlet. Assume the process is
adiabatic, aergonic, and steady flow.
14.* Water vapor enters a diffuser at a pressure of 0.070 MPa, a
temperature of 150.°C, and a velocity of 100 m/s. The inlet area of
the diffuser is 0.100 m 2 . By removing 288.2 kJ/kg in the form of
heat across the duct walls, the velocity is reduced to 1.00 m/s and
the pressure is increased to 0.200 MPa at the outlet. Determine the
outlet area of the diffuser.
15. Air at 70.0°F, 30.0 psia, and a velocity of 3.00 ft/s enters an
insulated steady state nozzle. The inlet area of the nozzle is
0.0500 m 2 . The nozzle contains an operating 1500. W electrical
heater. The air exits the nozzle at 14.7 psia and 300. ft/s.
Determine the temperature of the air at the exit of the nozzle.
Assume ideal gas behavior with constant specific heats and
neglect any changes in flow stream potential energy.
16.* Air at 20.0°C, 0.500 MPa, and a velocity of 1.00 m/s enters an
insulated nozzle. The inlet area of the nozzle is 0.0500 m 2 .The
nozzle contains an operating 500. W electrical resistance heater.
The air exits the nozzle at atmospheric pressure and 100. m/s.
Assuming ideal gas behavior with constant specific heats,
determine the exit temperature.
17. Air at 70.0°F and 30.0 psia enters an insulated nozzle with a
mass flow rate of 3.00 lbm/s. The nozzle contains an operating
1000. W electrical resistance heater. The air exits the nozzle at
14.7 psia. The inlet and exit areas of the nozzle are 0.500 and
0.100 ft 2 , respectively. Determine the velocity and temperature
of the air at the exit of the nozzle. Assume air to be an ideal gas.
18. The adiabatic, aergonic throttling calorimeter shown in Figure
6.23 is a device by which the quality of wet steam flowing in a
pipe may be determined. Determine (a) the enthalpy of the
steam in the pipe and (b) the quality of the steam in the pipe.