Modern Engineering Thermodynamics

444 CHAPTER 12: Mixtures of Gases and Vapors
First, the air passes over a cooling coil, where it is cooled below
its dew point temperature and the water condenses out until the
desired humidity ratio is reached. Then, the air is passed over a
reheating coil until its temperature reaches 71.0°F. Determine
a. The amount of water removed per pound of dry air passing
through the device.
b. The heat removed by the cooling coil in Btu/(lbm dry air).
c. The heat added by the reheating coil in Btu/(lbm dry air).
43.* An airstream with a mass flow rate of 2.00 kg/s, a dry bulb
temperature of 10.0°C, and a wet bulb temperature of 8.00°C is
mixed with an airstream having a mass flow rate of 1.00 kg/s, a
dry bulb temperature of 40.0°C, and a wet bulb temperature of
35.0°C. For the resulting mixture, determine the (a) humidity
ratio, (b) psychrometric enthalpy, (c) relative humidity, (d) dry
bulb temperature, (e) wet bulb temperature, and (f) dew point
temperature.
44.* Exactly 200 m 3 /min of air with a dry bulb temperature of
7.00°C and a wet bulb temperature of 5.00°C is continuously
mixed with 500. m 3 /min of air with a dry bulb temperature
of 32.0°C and a relative humidity of 60.0%. The mixing
chamber is at atmospheric pressure and is electrically heated
with a power consumption of 3.00 kW. For the resulting
mixture, determine (a) the dry bulb temperature, (b) the wet
bulb temperature, (c) the dew point temperature, and (d) the
relative humidity.
45.* 100. kg of atmospheric air (whose composition is given in
Example 12.2) is cooled in a 0.500 m 3 constant volume
container to 200. K. Determine the mixture pressure using
Dalton’s compressibility factor. Compare this result with that
obtained by assuming ideal gas (i.e., Z m = 1.00) behavior.
46. Show that the ratio of the Amagat specific volume, v Ai = V Ai /m i ,
to the Dalton specific volume, v Di = V m /m i , of gas i can be
written as v Ai /v Di = Z Ai p Di /Z Di p m .
47.* Atmospheric air, whose composition is given in Example 12.2, is
compressed to 1000. atm at 0.00°C. Determine the density of
the compressed air using Amagat’s compressibility factor and
compare this result with that obtained by assuming ideal gas
(i.e., Z m = 1.00) behavior.
48.* In normal psychrometric analysis at or below atmospheric
pressure, both the air and the water vapor are treated as ideal
gases. However, at high pressures, this assumption is no longer
valid. Determine the relative humidity (ϕ) that results when
10.0 g of water are added to 1.00 kg of dry air at a total pressure
of 10.0 MPa at 350.°C. Assume Amagat’s compressibility factor is
valid here and compare your result with that obtained by
assuming ideal gas behavior.
49.* 0.500 m 3 of a mixture of 35.0% acetylene (C 2 H 2 ), 25.0%
oxygen (O 2 ), 20.0% hydrogen (H 2 ), and 20.0% sulfur dioxide
(SO 2 ) on a mass basis is to be adiabatically compressed in a
piston-cylinder arrangement from 1.00 atm, 20.0°C to 100. atm
and 300.°C.
a. Using Kay’s law, find the final volume of the mixture.
b. Assuming constant specific heats, determine the work
required per unit mass of mixture.
50.* A mixture of 80.0% methane and 20.0% ethane on a molar
basis is contained in an insulated 1.00 m 3 tank at 3.00 MPa
and 50.0°C. An automatic flow control valve opens, causing
the tank pressure to drop quickly to 2.00 MPa before it closes
again.
a. Calculate the mass that escaped from the tank using Kay’s
law.
b. Determine the equilibrium tank temperature when the
control valve closes, assuming that the gas remaining in the
tank underwent a reversible process.
51.* 6.00 kg of hydrogen gas (H 2 ) is mixed with 28.0 kg of nitrogen
gas (N 2 ) and compressed to 40.5 MN/m 2 at 300.°C. At this
state, the specific volume of the mixture is measured and found
to be 0.0160 m 3 /kg. Determine the specific volume of this state
as predicted by each of the following models and calculate the
percent deviation from the measured value.
a. Ideal gas model.
b. Dalton’s law compressibility factor.
c. Amagat’s law compressibility factor.
d. Kay’s law.
52.* Determine the total mixture volume when 1 kgmole each of
hydrogen (H 2 ) and helium (He) gases are mixed at 15.0 atm
and 40.0 K, using
a. Dalton’s law compressibility factor.
b. Amagat’s law compressibility factor.
c. Kay’s law.
d. Which of the three results do you believe is the most
accurate, and why?
Design Problems
The following are open-ended design problems. The objective is to
carry out a preliminary thermal design as indicated. A detailed
design with working drawings is not expected unless otherwise specified.
These problems do not have specific answers, so each student’s
designisunique.
53. Design an electrically driven sling psychrometer to produce the
wet and dry bulb temperatures on digital readouts. The
finished product must cost less than 30.0 h of minimum wage
pay and be battery powered. If possible, fabricate and test your
design. (Suggestion: Try designing around inexpensive, “off the
shelf” components.)
54. Design an apparatus to measure the dew point of an air sample
based on the cooling of a mirrored surface until it fogs. If
possible, build and test this apparatus. (Suggestion: Consider
thermoelectric cooling of a polished metal plate.)
55.* Design a system to remove the respiration carbon dioxide from
inside a spacecraft and replace it with oxygen. Use a living
quarters volume of 10.0 m 3 with the crew generating a
maximum of 2.00 × 10 −5 m 3 /s of CO 2 . Assume the mixture
enters your system at 30.0°C and exits it at 20.0°C. Maintain
the same oxygen partial pressure in your mixture as that in
atmospheric air at 0.1013 MPa and 20.0°C.
56.* Design a system to remove the respiration carbon dioxide
from inside a submarine and replace it with oxygen. The air
volume of the submarine is 1000. m 3 ,andthecrewcan
generate a maximum of 1.30 × 10 −3 m 3 /s of CO 2 .The
submarine must be able to achieve a depth of 300. m. Assume
the air mixture enters your system at 30.0°C and exits at
20.0°C. Maintain the oxygen partial pressure at all times in
your mixture equal to that in atmospheric air at 0.1013 MPa
and 20.0°C.