Modern Engineering Thermodynamics

402 CHAPTER 11: More Thermodynamic Relations
when the entropy production rate per unit mass flow rate is
0.538 kJ/(kg·K) and the mean cylinder external wall
temperature is 432 K.
47. An inventor claims that 700. ft · lbf was used to compress
0.450 lbm of air isothermally in a closed piston-cylinder
apparatus from 14.7 psia, 70.0°F to 2000. psia. Assuming ideal
gas behavior,
a. Is this process possible?
b. If not, what is the maximum possible compression pressure
that could be reached with this process?
48.* Determine the compressibility factor for methane at 20.0 MPa
and 0.00C.
49.* In 1879, the French physicist Emile Amagat generated
experimental data in a mine shaft at Verpilleux, France, for his
research on the compressibility of gases. There he used a vertical
column of mercury 327 m high to measure the compressibility
of nitrogen at a pressure of 430. atm. Assuming the temperature
at the bottom of the mine shaft was 30.0°C, use the
compressibility charts to determine the value of the
compressibility factor for nitrogen under these conditions.
50.* For air at 20.0°C, there is a unique pressure above p R =1.00
at which the compressibility factor is the same as that of an
ideal gas. Use the compressibility charts to determine this
pressure.
51.* For air at 20.0°C, use the compressibility charts to determine
the low pressure range in which the compressibility factor of air
differs from that of an ideal gas by no more than 2.00% (i.e.,
1.0 ≤ Z ≤ 0.980). Is it reasonable to assume ideal gas behavior
for air at pressures up to 3.45 MPa (500. psia)?
52. 200. lbm of carbon dioxide is to be put into a rigid 3.00 ft 3
tank at 87.5°F. Use the compressibility factor to determine the
final pressure.
53. Determine the ratio of v′ c /v c for the following substances:
(a) water vapor, (b) nitrogen, (c) propane, and (d) methane.
54.* Using the generalized charts, determine the sum of the heat
transfer rate and power required to isothermally compress
0.300 kg/s of hydrogen in a steady flow process from 2.00 to
20.0 atm at 50.0 K. Is it possible to carry out this process
adiabatically?
55.* Using the generalized charts, determine the entropy change as
0.730 kg of carbon monoxide is expanded from 35.0 MPa to
0.100 MPa in an isothermal process at 100. K.
56. Compare the specific volumes of water vapor obtained from the
steam tables to those obtained from the compressibility factor
charts (Figures 11.5–11.7) at the following states
a. 14.7 psia, 300.°F.
b. 6000. psia, 1000 °F.
c. 8000. psia, 2000.°F.
57. Compare the values of h 2 – h 1 and s 2 – s 1 for water vapor
obtained from (a) the gas tables (Table C.16c) and (b) the
generalized charts (Figures 11.9 and 11.11) with those obtained
from the steam tables for the following conditions: 14.7 psia,
300.°F (state 1) and 6000. psia, 1000.°F (state 2).
58. Use the generalized charts to calculate the heat transfer rate
required to cool 7.00 lbm/s of argon gas from 500.°F, 2000. psia
to 300.°F in a steady flow, constant pressure heat exchanger.
Assume the specific heats of argon are constant over this
temperature range.
59. Methane is throttled adiabatically with negligible velocity
change from 1500. psia, 70.0°F to atmospheric pressure.
Assuming constant specific heats and using the generalized
charts, determine the exit temperature.
60. Carbon dioxide is throttled adiabatically with negligible velocity
change from 2500. psia, 800. R to atmospheric pressure. Use
the generalized charts to determine the exit temperature by
a. Assuming constant specific heats.
b. Using the gas tables (Table C.16c).
61.* Helium in an external storage tank on a spacecraft is expanded
through an isentropic attitude control nozzle with a negligible
inlet velocity from 2.00 MPa, 10.0 K to 0.0100 MPa. Assuming
constant specific heats and using the generalized charts,
determine the exit temperature and velocity.
62.* Sulfur dioxide with a negligible inlet velocity is expanded
through an isentropic nozzle from 20.0 MPa, 500. K to 0.200
MPa in a chemical processing unit. Assuming constant specific
heats and using the generalized charts, determine the exit
temperature and velocity.
63. Hydrogen is cooled in an isobaric heat exchanger from 5000. to
527 R at 20.0 psia. The heat transfer occurs across an
isothermal wall at 500. R inside the heat exchanger. Use the
generalized charts to determine the hydrogen’s heat transfer
and entropy production rates per unit mass flow rate.
64. Use the generalized charts to determine the changes in specific
enthalpy and specific entropy of nitrogen as it undergoes an
isobaric cooling process from 2000. to 1000. R at 14.7 psia
assuming
a. Constant specific heats.
b. Temperature dependent specific heats.
c. Compute the percentage difference between the results of
parts a and b.
65.* According to Dalton’s law of partial pressures, the partial
pressure exerted by the water vapor in a mixture of air and water
vapor is equal to the pressure the water vapor would exert if it
alone occupied the total volume of the mixture. If 1.00 m 3 of
humid air at 20.0°C contains 10.3 g of water vapor, determine
a. The partial pressure of the water vapor.
b. The maximum partial pressure of water vapor at this
temperature.
c. The ratio of the answer in part a to that of part b (this ratio
is called the relative humidity of the air).
66. Steam is throttled from 100. psia, 500.°F to 14.7 psia in an
isenthalpic process. Determine the change in specific entropy
and the exit temperature of the steam using
a. Ideal gas equations.
b. The steam tables.
c. Compute the percent error in assuming ideal gas behavior.
67.* In the warp drive system of an intergalactic spacecraft, 13.0 kg/s
of water vapor is reversibly and isothermally expanded from
500. to 125 Pa at 100.°C. Determine the heat transfer rate and
the power produced. Assume ideal gas behavior.
68. Water vapor is heated from 300. to 400.°F in a steady flow
isobaric process. Determine the percent error in calculating the
heat transfer rate per unit mass flow rate by using the ideal gas
equations for system pressures of (a) 20.0 psia, (b) 2.00 psia,
and (c) 0.200 psia.
69.* Saturated water vapor at 10.0 kPa is expanded reversibly and
isentropically in a steady flow process in a doorknob heat treating
plant to 5.00 kPa. Determine the final temperature, the heat
transfer rate, and the power produced per unit mass flow rate.
Assume the steam is an ideal gas.