Modern Engineering Thermodynamics

164 CHAPTER 5: First Law Closed System Applications
41.* When the pressure on saturated liquid water is suddenly
reduced to a lower pressure in an adiabatic and aergonic
process, the liquid’s temperature must also be reduced to reach
a new equilibrium state. Consequently, part of the initial liquid
is very quickly converted into a saturated vapor at the lower
pressure, and the resulting heat of vaporization cools the
remaining liquid to the proper temperature. Vapor formed in
this manner is called flash steam, because the liquid appears to
“flash” into a vapor as the pressure is reduced. Determine the
final temperature and the percent of flash steam produced as a
closed system containing saturated liquid water suddenly bursts
and the pressure drops from 1.00 to 0.100 MPa in an adiabatic
and aergonic process.
42. In 1798, the American Benjamin Thompson (Count Rumford,
1753−1814) carried out a series of cannon-boring experiments in
which he established that heat was not a material substance. (It
was commonly believed at that time that heat was a colorless,
odorless, weightless fluid called caloric.) In his third experiment,
he noted that the “total quantity of ice-cold water which with the
heat actually generated by friction, and accumulated in 2 h 30 m ,
might have been heated 180°, or made to boil, = 26.58 lb.” He
also stated that “the machinery used in the experiment could
easily be carried round by the force of one horse.” Use this crude
data of Rumford to estimate the mechanical equivalent of heat
(i.e., the number of ft · lbf per Btu). Take the specific heat of
liquid water to be 1.00 Btu/(lbm · R).
43. The mechanical equivalent of heat (i.e., the number of ft · lbf per
Btu) was first established accurately by James Prescott Joule
(1818–1889) in a long series of experiments carried out between
1849 and 1878. In one of his first experiments, the work done by
falling weights caused the rotation of a paddle wheel immersed
in water. The weights had a mass of 57.8 lbm and fell 105 ft. The
resulting paddle wheel motion caused an increase in temperature
of 0.563°F in 13.9 lbm of water in an insulated container. Using
a specific heat of c = 1.00 Btu/(lbm · R), determine the
mechanical equivalent of heat from these early data of Joule.
44. Determine the heat generated (in Btu/year) by the brakes of
100. million 3000. lbm automobiles that isothermally brake to
a stop on a horizontal surface from 55.0 mph ten times per day.
Convert your answer into equivalent barrels of crude oil per year
then into quads per year, where one barrel of crude oil contains
5.80 × 10 6 Btu of energy and one quad is defined to be exactly
10 15 Btu.
45.* An insulated vessel contains an unknown amount of ammonia.
A 600. W electrical heater is put into the vessel and turned on
for 30.0 min. The heater raises the temperature of the ammonia
from 20.0 to 100.°C in a constant pressure process at 100. kPa.
Determine the mass of ammonia in the vessel.
46. Using the general energy rate balance equation for a closed
system, show that, under adiabatic, isothermal, and aergonic
conditions, the acceleration of an object falling vertically
downward in a vacuum is simply the local acceleration of
gravity, g.
47.* Determine the difference in water temperature between the
top and the bottom of a waterfall 35.0 m high. Choose as
your system 1.00 kg of water at the top of the falls and
follow its change of state as it moves to the bottom of the
falls. Assume water to be an incompressible liquid and neglect
any heat loss. Also assume a constant water velocity for this
process.
48. In days of yore, a bow and arrows were an archer’s best friend.
Determine
a. The maximum velocity of a 0.400 lbm arrow shot
horizontally from a bow in which 100. ft · lbf is required to
draw back the arrow before releasing it.
b. The maximum height this arrow would reach if aimed
vertically.
49.* A 5.00 cm diameter steel sphere initially at 20.0°C istobe
heated by immersing it in boiling water at 100.°C with a
convective heat transfer coefficient of 2000. W/(m 2 ·K).
Determine the time required to raise the bulk temperature of the
sphere to 90.0°C. The specific heat of the steel is 0.500 kJ/(kg·K)
and its density is 7800. kg/m 3 .
50.* An asteroid enters the Earth’s atmosphere and descends
vertically with a constant velocity of 100. m/s. Determine the
rate of change of the asteroid’s temperature at the point where
its temperature exactly equals the surrounding air temperature.
The specific heat of the asteroid is 0.300 kJ/(kg· K).
51.* 50,000. kg of saturated liquid water at 20.0°C is to be heated in
a mass-energy conversion oven in which 1.00 × 10 –6 kg of mass
is converted into pure thermal energy (Q = mc 2 ). Assuming that
the water is an incompressible liquid with a specific heat of
4.20 kJ/(kg · K), determine the final temperature of the water.
The velocity of light is 2.998 × 10 8 m/s.
52. A hand grenade contains 1.90 ounces (0.120 lbm) of TNT.
Determine the number of hand grenades it would take to
produce an explosion equivalent to the Brockton shoe factory
boiler explosion discussed in Example 5.8. The explosive energy
of TNT is 1400. Btu/lbm.
53. Between 1897 and 1927, the Stanley brothers of Newton, Maine,
manufactured steam-powered automobiles. They had a steam
boiler 23.0 inches in diameter and 14.0 inches high that contained
steam at 600. psia and 600.°F. Determine the explosive energy of
these boilers and the number of 1.00 lbm sticks of TNT that would
contain the equivalent amount of explosive energy. Assume the
ambient temperature is 70.0°F.
54. The greatest steam explosion in history is thought to have occurred
on August 27, 1883, when the volcano Krakatoa in Sunda Strait,
Indonesia, erupted and its molten lava vaporized an estimated
1mi 3 of seawater. The entire 2600. ft high mountain was
disintegrated and a crater 1000. ft deep was produced. More than
36,000. people were killed, most by the 120. ft tidal wave created
by the eruption. Assuming that the seawater is simply saturated
liquid water at 60.0°F, determine the number of tons of TNT that
would have the same explosive energy as this eruption. For
reference, the total military production of explosives for both
world wars was equivalent to 32.0 million tons of TNT. The
explosive energy of TNT is 1400. Btu/lbm.
55. Show that, if a pressure vessel filled with a constant specific heat
ideal gas ruptures and the gas follows a polytropic process during
the subsequent depressurization, then the maximum explosive
energy of this system can be written as
Γ max = p initial / ðk − 1Þ
56. Consider a gaseous star undergoing a gravitational collapse.
Assume the star to be a closed system and composed of an ideal
gas with constant specific heats. The collapse process is given by
the relations
v/r 3 = constant and Tr = constant