Modern Engineering Thermodynamics

162 CHAPTER 5: First Law Closed System Applications
Assume the room air is at 14.7 psia and 70.0°F during the entire
process.
13.* The human body under the stress of exercise can release 230. W
as heat. Assume the human body to be a closed system and
neglect any work or change in kinetic energy. Determine the rate
of change in internal energy of the human body as a 68.0 kg
person runs at a constant velocity up a staircase having a vertical
height of 15.0 m in 60.0 s.
14.* Exactly 14.0 kg of herpes duplex virus scum is compressed
from a volume of 4.50 to 1.50 m 3 in a process where p is in
N/m 2 is given by p = 60:0/V + 30:0, when V is in m 3 . During
the compression process the virus gives off 20.0 J of heat and
turns a putrid yellow in color. Determine the change in the
specific internal energy of the virus for this process.
15.* Exactly 3.70 kg of nitrogen gas at exactly 0°C and 0.100 MPa is
put into a cylinder with a piston and compressed in a process
defined by pV 2 = constant. When the final pressure in the
cylinder reaches 10.0 MPa, and assuming ideal gas behavior,
determine (a) the amount of work done on the nitrogen by the
piston and (b) the final temperature of the nitrogen.
16. Heat is transferred to 0.100 lbm of air contained in a frictionless
piston-cylinder apparatus until its volume expands from an
initial value of 1.00 ft 3 to a final value of 1.50 ft 3 . Calculate the
work transport of energy and the heat transfer when the system
is the air in the cylinder. The initial temperature of the air is
70.0°F. Consider air to be an ideal gas.
17. Exactly 0.100 lbm of air (an ideal gas) initially at 50.0 psia and
100.°F in a cylinder with a movable piston undergoes the
following two-part process. First, the air is expanded
adiabatically to 30.0 psia and 24.0°F, then it is compressed
isobarically (i.e., at constant pressure) to half its initial volume.
Determine
a. The final temperature at the end of the isobaric compression.
b. The work produced during the adiabatic expansion.
c. The heat transfer during the isobaric compression.
18.* A 1000. kg battery powered adiabatic electric vehicle has a fully
charged battery containing 20.0 MJ of stored energy. If it
requires 12.0 kW of power to keep it moving at a constant
velocity on a horizontal road, determine how long the vehicle
will operate before its battery is fully discharged.
19. How many watt hours of electricity are needed to heat the
contents of a sealed, rigid, insulated chamber pot containing
0.300 lbm of water from 50.0°F with a quality of 1.00% to a
saturated vapor. The chamber pot has an internal electrical
resistance heater with a power cord that plugs into a standard
110. V ac outlet.
20.* A small, sealed, rigid container holding 0.500 kg of water is
heated in a microwave oven drawing 1600. W at 2460 MHz.
The oven’s timer is set for exactly 1 min. The initial
thermodynamic state of the water is 20.0°C at 1.00 atm. After
the 1 min heating period, determine (a) the water’s work
transport of energy, (b) the water’s heat transport of energy,
(c) the change in specific internal energy of the water, and (d) the
final temperature and pressure assuming the liquid water to be
an incompressible liquid with a specific heat of 4.50 kJ/(kg·K).
21.* 30.5 kg of H 2 O contained in a 1.00 m 3 rigid tank are at an
initial pressure of 10.0 MPa. The contents of the tank are cooled
at constant volume until a final pressure of 2.00 MPa is reached.
Determine the final temperature, the final value of the specific
internal energy, and the process heat transfer.
22. A small rigid tank 1.00 ft 3 in volume contains saturated water
vapor at 300.°F. An initially evacuated rigid container 3.4549 ft 3
in volume is then attached to the first tank and the
interconnecting valve is opened. The combined system is then
brought to equilibrium at 300.°F by an appropriate heat
transport of energy. Determine the final pressure in the system
and the required heat transfer.
23. A pressure vessel that has a volume of 0.200 ft 3 is filled with
saturated liquid Refrigerant-22 at 70.0°F. An evacuated container
4.00 ft 3 in volume is attached to the vessel and the
interconnecting valve is opened. The combined system is then
brought to equilibrium at 70.0°F Calculate the heat transport of
energy to (or from) the system.
24.* A mixture of hydrazine and cow manure happens to have the
same thermodynamic properties as pure water. A secret process
requires that this mixture be vaporized then injected into light
bulbs. Determine the work and heat transport of energy that
occurs when 1.30 kg of this mixture is isothermally converted
from a saturated liquid to a saturated vapor at 40.0°C.
25. A lead bullet weighing 0.0200 lbf and traveling horizontally at
3000. ft/s is suddenly stopped by a perfectly rigid object that
does not deform during the impact. Find the temperature rise of
the bullet assuming the impact occurs so rapidly that the impact
process can be considered to be adiabatic. For lead, use
Δu = 0.0130(ΔT) in Btu/lbm, where T is in °F orR.
26. As a bullet travels down the barrel of a pistol, the pressure from
the burning propellant behind it increases linearly with the
volume V displaced by the bullet as p = V × 10 3 in psia, where V
is in in. 3 . The total volume of the barrel is πR 2 L, where R is the
radius of the bore and L is its total length. Determine the velocity
of the bullet at the end of the barrel if it travels horizontally and
adiabatically down the barrel without changing its internal
energy and with no friction.
Data
Barrel length = 6.00 in
Barrel diameter = 0.380 in
Bullet mass = 5.00 g
27. A rubber band weighing 1.00 × 10 –3 lbf that obeys Hooke’s law
of elasticity is stretched horizontally and adiabatically from an
initial length of 3.00 to 4.00 in.
a. Determine the change in total internal energy of the rubber
band when it is stretched, if its elastic modulus is 1.00 ×
10 3 lbf/in 2 and its cross-sectional area remains approximately
constant at 7.80 × 10 –3 in 2 .
b. If the stretched rubber band is suddenly released horizontally
and adiabatically, determine its final velocity neglecting air
friction and any height change during its flight.
28. A thin glass sphere 0.0250 ft 3 in volume is completely filled
with 1.00 lbm of saturated liquid nitrogen. The glass sphere is
sealed inside a large rigid, evacuated, insulated container whose
volume is 10.0 ft 3 . What are the final pressure and quality
(if any) inside the larger container if the glass sphere breaks.
29. 1.00 ft 3 of saturated liquid water at 14.7 psia is poured into an
initially evacuated, rigid, insulated vessel whose volume is 100. ft 3 .
Inside the vessel is an electric heater that draws an effective 10.0 A
at an effective 110. V. Once this heater is turned on, how long will
it take the contents of the vessel to reach 40.0 psia?
30.* A rigid vessel having a volume of 3.00 m 3 initially contains steam
at 0.400 MPa and a quality of 40.2%. If 23.79 MJ of heat is added
to the steam, determine its final pressure and temperature.