Home > Articles > Engineering

This chapter is from the book

This chapter is from the book

Introductory Chemical Engineering Thermodynamics, 2nd EditionIntroductory Chemical Engineering Thermodynamics, 2nd Edition

Learn More Buy

This chapter is from the book

This chapter is from the book

Introductory Chemical Engineering Thermodynamics, 2nd EditionIntroductory Chemical Engineering Thermodynamics, 2nd Edition

Learn More Buy

1.8 Homework Problems

Note: Some of the steam table homework problems involve enthalpy, H, which is defined for convenience using properties discussed in this chapter, H u2261.gif U + PV. The enthalpy calculations can be performed by reading the tabulated enthalpy values from the tables in an analogous manner used for internal energy. We expect that students will be introduced to this property in course lectures in parallel with the homework problems that utilize H.

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.

InformIT Promotional Mailings & Special Offers

I would like to receive exclusive offers and hear about products from InformIT and its family of brands. I can unsubscribe at any time.

Overview


Pearson Education, Inc., 221 River Street, Hoboken, New Jersey 07030, (Pearson) presents this site to provide information about products and services that can be purchased through this site.

This privacy notice provides an overview of our commitment to privacy and describes how we collect, protect, use and share personal information collected through this site. Please note that other Pearson websites and online products and services have their own separate privacy policies.

Collection and Use of Information


To conduct business and deliver products and services, Pearson collects and uses personal information in several ways in connection with this site, including:

Questions and Inquiries

For inquiries and questions, we collect the inquiry or question, together with name, contact details (email address, phone number and mailing address) and any other additional information voluntarily submitted to us through a Contact Us form or an email. We use this information to address the inquiry and respond to the question.

Online Store

For orders and purchases placed through our online store on this site, we collect order details, name, institution name and address (if applicable), email address, phone number, shipping and billing addresses, credit/debit card information, shipping options and any instructions. We use this information to complete transactions, fulfill orders, communicate with individuals placing orders or visiting the online store, and for related purposes.

Surveys

Pearson may offer opportunities to provide feedback or participate in surveys, including surveys evaluating Pearson products, services or sites. Participation is voluntary. Pearson collects information requested in the survey questions and uses the information to evaluate, support, maintain and improve products, services or sites, develop new products and services, conduct educational research and for other purposes specified in the survey.

Contests and Drawings

Occasionally, we may sponsor a contest or drawing. Participation is optional. Pearson collects name, contact information and other information specified on the entry form for the contest or drawing to conduct the contest or drawing. Pearson may collect additional personal information from the winners of a contest or drawing in order to award the prize and for tax reporting purposes, as required by law.

Newsletters

If you have elected to receive email newsletters or promotional mailings and special offers but want to unsubscribe, simply email information@informit.com.

Service Announcements

On rare occasions it is necessary to send out a strictly service related announcement. For instance, if our service is temporarily suspended for maintenance we might send users an email. Generally, users may not opt-out of these communications, though they can deactivate their account information. However, these communications are not promotional in nature.

Customer Service

We communicate with users on a regular basis to provide requested services and in regard to issues relating to their account we reply via email or phone in accordance with the users' wishes when a user submits their information through our Contact Us form.

Other Collection and Use of Information


Application and System Logs

Pearson automatically collects log data to help ensure the delivery, availability and security of this site. Log data may include technical information about how a user or visitor connected to this site, such as browser type, type of computer/device, operating system, internet service provider and IP address. We use this information for support purposes and to monitor the health of the site, identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents and appropriately scale computing resources.

Web Analytics

Pearson may use third party web trend analytical services, including Google Analytics, to collect visitor information, such as IP addresses, browser types, referring pages, pages visited and time spent on a particular site. While these analytical services collect and report information on an anonymous basis, they may use cookies to gather web trend information. The information gathered may enable Pearson (but not the third party web trend services) to link information with application and system log data. Pearson uses this information for system administration and to identify problems, improve service, detect unauthorized access and fraudulent activity, prevent and respond to security incidents, appropriately scale computing resources and otherwise support and deliver this site and its services.

Cookies and Related Technologies

This site uses cookies and similar technologies to personalize content, measure traffic patterns, control security, track use and access of information on this site, and provide interest-based messages and advertising. Users can manage and block the use of cookies through their browser. Disabling or blocking certain cookies may limit the functionality of this site.

Do Not Track

This site currently does not respond to Do Not Track signals.

Security


Pearson uses appropriate physical, administrative and technical security measures to protect personal information from unauthorized access, use and disclosure.

Children


This site is not directed to children under the age of 13.

Marketing


Pearson may send or direct marketing communications to users, provided that

  • Pearson will not use personal information collected or processed as a K-12 school service provider for the purpose of directed or targeted advertising.
  • Such marketing is consistent with applicable law and Pearson's legal obligations.
  • Pearson will not knowingly direct or send marketing communications to an individual who has expressed a preference not to receive marketing.
  • Where required by applicable law, express or implied consent to marketing exists and has not been withdrawn.

Pearson may provide personal information to a third party service provider on a restricted basis to provide marketing solely on behalf of Pearson or an affiliate or customer for whom Pearson is a service provider. Marketing preferences may be changed at any time.

Correcting/Updating Personal Information


If a user's personally identifiable information changes (such as your postal address or email address), we provide a way to correct or update that user's personal data provided to us. This can be done on the Account page. If a user no longer desires our service and desires to delete his or her account, please contact us at customer-service@informit.com and we will process the deletion of a user's account.

Choice/Opt-out


Users can always make an informed choice as to whether they should proceed with certain services offered by InformIT. If you choose to remove yourself from our mailing list(s) simply visit the following page and uncheck any communication you no longer want to receive: www.informit.com/u.aspx.

Sale of Personal Information


Pearson does not rent or sell personal information in exchange for any payment of money.

While Pearson does not sell personal information, as defined in Nevada law, Nevada residents may email a request for no sale of their personal information to NevadaDesignatedRequest@pearson.com.

Supplemental Privacy Statement for California Residents


California residents should read our Supplemental privacy statement for California residents in conjunction with this Privacy Notice. The Supplemental privacy statement for California residents explains Pearson's commitment to comply with California law and applies to personal information of California residents collected in connection with this site and the Services.

Sharing and Disclosure


Pearson may disclose personal information, as follows:

  • As required by law.
  • With the consent of the individual (or their parent, if the individual is a minor)
  • In response to a subpoena, court order or legal process, to the extent permitted or required by law
  • To protect the security and safety of individuals, data, assets and systems, consistent with applicable law
  • In connection the sale, joint venture or other transfer of some or all of its company or assets, subject to the provisions of this Privacy Notice
  • To investigate or address actual or suspected fraud or other illegal activities
  • To exercise its legal rights, including enforcement of the Terms of Use for this site or another contract
  • To affiliated Pearson companies and other companies and organizations who perform work for Pearson and are obligated to protect the privacy of personal information consistent with this Privacy Notice
  • To a school, organization, company or government agency, where Pearson collects or processes the personal information in a school setting or on behalf of such organization, company or government agency.

Links


This web site contains links to other sites. Please be aware that we are not responsible for the privacy practices of such other sites. We encourage our users to be aware when they leave our site and to read the privacy statements of each and every web site that collects Personal Information. This privacy statement applies solely to information collected by this web site.

Requests and Contact


Please contact us about this Privacy Notice or if you have any requests or questions relating to the privacy of your personal information.

Changes to this Privacy Notice


We may revise this Privacy Notice through an updated posting. We will identify the effective date of the revision in the posting. Often, updates are made to provide greater clarity or to comply with changes in regulatory requirements. If the updates involve material changes to the collection, protection, use or disclosure of Personal Information, Pearson will provide notice of the change through a conspicuous notice on this site or other appropriate way. Continued use of the site after the effective date of a posted revision evidences acceptance. Please contact us if you have questions or concerns about the Privacy Notice or any objection to any revisions.

Last Update: November 17, 2020