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1.8 Homework Problems

1.1

In each of the following, sketch your estimates of the intermolecular potentials between the given molecules and their mixture on the same pair of axes.

  1. Chloroform is about 20% larger than acetone and about 10% stickier, but chloroform and acetone stick to one another much more strongly than they stick to themselves.
  2. You have probably heard that "oil and water don't mix." What does that mean in molecular terms? Let's assume that oil can be characterized as benzene and that benzene is four times larger than water, but water is 10% stickier than benzene. If the ε12 parameter is practically zero, that would represent that the benzene and water stick to themselves more strongly than to one another. Sketch this.

1.2

For each of the states below, calculate the number of moles of ideal gas held in a three liter container.

  1. T = 673 K, P = 2 MPa
  2. T = 500 K, P = 0.7 MPa
  3. T = 450 K, P = 1.5 MPa

1.3

A 5 m3 outdoor gas storage tank warms from 10°C to 40°C on a sunny day. If the initial pressure was 0.12 MPa at 10°C, what is the pressure at 40°C, and how many moles of gas are in the tank? Use the ideal gas law.

1.4

An automobile tire has a pressure of 255 kPa (gauge) in the summer when the tire temperature after driving is 50°C. What is the wintertime pressure of the same tire at 0°C if the volume of the tire is considered the same and there are no leaks in the tire?

1.5

A 5 m3 gas storage tank contains methane. The initial temperature and pressure are P = 1 bar, T = 18°C. Using the ideal gas law, calculate the P following each of the successive steps.

  1. 1 m3 (at standard conditions) is withdrawn isothermally.
  2. The sun warms the tank to 40°C.
  3. 1.2 m3 (at standard conditions) is added to the tank and the final temperature is 35°C.
  4. The tank cools overnight to 18°C.

1.6

Calculate the mass density of the following gases at 298 K and 1 bar.

  1. Nitrogen
  2. Oxygen
  3. Air (use average molecular weight)
  4. CO2
  5. Argon

1.7

Calculate the mass of air (in kg) that is contained in a classroom that is 12m x 7m x 3m at 293 K and 0.1 MPa.

1.8

Five grams of the specified pure solvent is placed in a variable volume piston. What is the volume of the pure system when 50% and 75% have been evaporated at: (i) 30°C, (ii) 50°C? Use the Antoine equation (Appendix E) to relate the saturation temperature and saturation pressure. Use the ideal gas law to model the vapor phase. Show that the volume of the system occupied by liquid is negligible compared to the volume occupied by vapor.

  1. Hexane (ρL = 0.66 g/cm3)
  2. Benzene (ρL = 0.88 g/cm3)
  3. Ethanol (ρL = 0.79 g/cm3)
  4. Water without using the steam tables (ρL = 1 g/cm3)
  5. Water using the steam tables

1.9

A gasoline spill is approximately 4 liters of liquid. What volume of vapor is created at 1 bar and 293 K when the liquid evaporates? The density of regular gasoline can be estimated by treating it as pure isooctane (2,2,4-trimethylpentane ρL = 0.692 g/cm3) at 298 K and 1 bar.

1.10

The gross lifting force of a balloon is given by (ρair – ρgas)Vballoon. What is the gross lifting force (in kg) of a hot air balloon of volume 1.5E6 L, if the balloon contains gas at 100°C and 1 atm? The hot gas is assumed to have an average molecular weight of 32 due to carbon dioxide from combustion. The surrounding air has an average molecular weight of 29 and is at 25°C and 1 atm.

1.11

LPG is a useful fuel in rural locations without natural gas pipelines. A leak during the filling of a tank can be extremely dangerous because the vapor is denser than air and drifts to low elevations before dispersing, creating an explosion hazard. What volume of vapor is created by a leak of 40L of LPG? Model the liquid before leaking as propane with ρL = 0.24 g/cm3. What is the mass density of pure vapor propane after depressurization to 293 K and 1 bar? Compare with the mass density of air at the same conditions.

1.12

The gas phase reaction A u2192.gif 2R is conducted in a 0.1 m3 spherical tank. The initial temperature and pressure in the tank are 0.05 MPa and 400 K. After species A is 50% reacted, the temperature has fallen to 350 K. What is the pressure in the vessel?

1.13

A gas stream entering an absorber is 20 mol% CO2 and 80 mol% air. The flowrate is 1 m3/min at 1 bar and 360 K. When the gas stream exits the absorber, 98% of the incoming CO2 has been absorbed into a flowing liquid amine stream.

  1. What are the gas stream mass flowrates on the inlet and outlets in g/min?
  2. What is the volumetric flowrate on the gas outlet of the absorber if the stream is at 320 K and 1 bar?

1.14

A permeation membrane separates an inlet air stream, F, (79 mol% N2, 21 mol% O2), into a permeate stream, M, and a reject stream, J. The inlet stream conditions are 293 K, 0.5 MPa, and 2 mol/min; the conditions for both outlet streams are 293 K and 0.1 MPa. If the permeate stream is 50 mol% O2, and the reject stream is 13 mol% O2, what are the volu-metric flowrates (L/min) of the two outlet streams?

1.15

  1. What size vessel holds 2 kg water at 80°C such that 70% is vapor? What are the pressure and internal energy?
  2. A 1.6 m3 vessel holds 2 kg water at 0.2 MPa. What are the quality, temperature, and internal energy?

1.16

For water at each of the following states, determine the internal energy and enthalpy using the steam tables.

T(°C)

P(MPa)

(a)

100

0.01

(b)

550

6.25

(c)

475

7.5

(d)

180

0.7

1.17

Determine the temperature, volume, and quality for one kg water under the following conditions:

  1. U = 3000 kJ/kg, P = 0.3 MPa
  2. U = 2900 kJ/kg, P = 1.7 MPa
  3. U = 2500 kJ/kg, P = 0.3 MPa
  4. U = 350 kJ/kg, P = 0.03 MPa

1.18

Two kg of water exist initially as a vapor and liquid at 90°C in a rigid container of volume 2.42 m3.

  1. At what pressure is the system?
  2. What is the quality of the system?
  3. The temperature of the container is raised to 100°C. What is the quality of the system, and what is the pressure? What are ΔH and ΔU at this point relative to the initial state?
  4. As the temperature is increased, at what temperature and pressure does the container contain only saturated vapor? What is ΔH and ΔU at this point relative to the initial state?
  5. Make a qualitative sketch of parts (a) through (d) on a P-V diagram, showing the phase envelope.

1.19

Three kg of saturated liquid water are to be evaporated at 60°C.

  1. At what pressure will this occur at equilibrium?
  2. What is the initial volume?
  3. What is the system volume when 2 kg have been evaporated? At this point, what is ΔU relative to the initial state?
  4. What are DH and ΔU relative to the initial state for the process when all three kg have been evaporated?
  5. Make a qualitative sketch of parts (b) through (d) on a P-V diagram, showing the phase envelope.
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