Modern Engineering Thermodynamics

Problems 441
Problems (* indicates problems in SI units)
1.* 1.00 kg of CH 4 , 6.30 kg of O 2 , and 13.2 kg of N 2 are combined
to form a gas mixture. Find the molecular mass of the mixture.
2. Ammonia gas is flowing in a tube whose cross-sectional area is
1.00 ft 2 . The density of the ammonia is 0.100 lbm/ft 3 . At some
point in the system, CO 2 is added at a rate of 1.00 × 10 −3 lbm/h
in a steady flow process. At a point further downstream,
a detector indicates that the concentration of CO 2 on a mass basis
is 1.00 × 10 −3 %. Determine the inlet velocity of the ammonia.
3. The following is the gravimetric analysis of a gaseous mixture:
Constituent
N 2 60.0
CO 2 22.0
CO 11.0
O 2 7.00
Find the mole fractions of the components in the mixture.
4. If the amount of helium produced by the large-scale
liquefaction of air is 1.30 lbm per 100. tons of air, determine
the mass, mole, and volume fractions of helium in air. Assume
air is a mixture of ideal gases.
5.* A mixture of air and water vapor at 20.0°C and 0.101 MPa has a
relative humidity of 100.%. Using the information given in
Example 12.2, determine
a. The molar composition.
b. The effective molecular mass.
c. The mass concentration.
d. The effective gas constant of the mixture, whose components
are nitrogen, oxygen, water vapor, argon, and carbon
dioxide.
6. A gas bulb of volume 0.100 ft 3 contains hydrogen at a pressure
of 10.0 psia and a temperature of 50.0°F. Nitrogen is introduced
into the bulb such that the final pressure is 20.0 psia and the
final temperature is 80.0°F. Find the mole fraction and the mass
fraction of the hydrogen in the final state.
7. Using Eqs. (12.11), (12.12), and (12.15), show that the
equivalent gas constant of a mixture R m can be determined
directly from the mass and mole fraction compositions (w i and
x i ) and the species gas constants ðR i = R/M i Þ as
a. R m = ∑w i R i
b. R m =
1
∑ðx i /R i Þ
% by mass
8. A mixture of ideal gases at a total pressure of 40.0 psia and
70.0°F contains 0.600 lbm of hydrogen (H 2 ) and 4.80 lbm of
oxygen (O 2 ). Determine
a. The mole fraction of the hydrogen in the mixture.
b. The equivalent molecular mass of the mixture.
c. The total volume occupied by the mixture under the
conditions stated.
9.* (a) How many kg of nitrogen must be mixed with 5.00 kg of
carbon dioxide to produce an ideal gas mixture that is 50.0%
by volume of each component? (b) For the resulting mixture
of part a, determine the mixture molecular mass (M m ), gas
constant (R m ), and the partial pressure of the nitrogen if that
of the carbon dioxide is 0.0700 MPa.
10. A furnace exhaust stack is instrumented so that a sample of the
stack gas can be analyzed for composition. The analysis gives
the following volume fractions: 70.0% N 2 , 20.0% CO 2 , 8.00%
CO, 1.00% Ar, and 1.00% H 2 O.
a. What is the molecular mass of the stack gas?
b. Calculate the mass fraction of each of the gases.
c. If the measured pressure in the stack is 15.0 psia, what is the
partial pressure of the carbon monoxide?
11.* The Department of Homeland Security discovered that 10.0 kg
of nitrogen (N 2 ) was mixed with 3.82 kg of a possibly toxic
unknown gas. The resulting mixture occupies a volume of 2.00 m 3
at 0.800 MPa and 65.0°C. Both gases and the mixture are ideal
gases. Determine
a. The molecular mass of the gas mixture.
b. The volume fraction of each gas present in the mixture.
12. Onboard a starship, a demented alien creature releases a mixture
of ideal gases made up of 4.00 lbm of molecular oxygen (O 2 )
and 6 lbm of an unknown and possibly toxic gas. Before the
gas mixture was released, you noticed that its original container
had a volume of 10.0 ft 3 , and at 150.°F, it had a pressure of
114.3 psia. Because you are a line officer engineer, the captain
asks you for your assessment of the situation. Is the gas lethal?
To draw a proper conclusion, you must determine
a. The molecular mass of the unknown gas.
b. The probable name of this gas.
c. The volume fraction of each gas present in the mixture.
13. The measured molecular masses of many naturally occurring
chemical elements differ appreciably from integer values due to
the presence of isotopes of the element in the test sample.
Commercially available neon has a measured molecular mass of
20.183. The gas is known to be a mixture of two isotopes
whose molecular masses are 20.0 and 22.0. Determine the mole
and mass fractions of each of the neon isotopes present in
commercial neon.
14. 1.00 ft 3 of steam at 300.°F and 14.7 psia is mixed with 3.00 ft 3
of methane at 80.0°F and 14.7 psia. Assuming ideal gas
behavior for both of these substances, determine
a) The mass fractions.
b) The mole fractions.
c) The pressure fractions.
d) Both the constant pressure and constant volume specific
heats of the mixture.
15. A rigid insulated tank is divided into two compartments by a
partition. Initially, 5.60 lbm of nitrogen is introduced into one
compartment at a pressure of 30.0 psia and a temperature of
140.°F. At the same time, 13.2 lbm of carbon dioxide is
introduced into the other compartment at a pressure of 15.0 psia
and a temperature of 60.0°F. The partition is then removed and
the gases are allowed to mix. Assuming ideal gas behavior, find
the pressure in the tank after the mixing.
16.* A perfect gas mixture consists of 3.00 kg of nitrogen (N 2 ) and
5.00 kg of carbon dioxide (CO 2 ) at a pressure of 1.00 MPa and
a temperature of 30.0°C. If the mixture is heated at constant
pressure to 40.0°C, find the work and the heat transfer required
for this process.
17.* We invented a new process in which 2.00 kg/min of hydrogen
at 5.00°C and 1.00 atm is continuously aergonically mixed with