Introduction to Chemical Engineering Coursework 1 Material Balances Question 1 (20%) Water enters a 2.00-m3 tank at a rate of 6.00 kg/s and is withdrawn at a rate of 3.00 kg/s. The tank is initially half full. (a) Is this process continuous, batch, or semibatch? Is it transient or steady state? (b) Write a mass balance for the process (see Example 4.2-1). Identify the terms of the general balance equation (Equation 4.2-1) present in your equation and state the reason for omitting any terms. (c) How long will the tank take to overflow? Solution 1 a) Continous, Transient b) Input – Output = Accumulation No reactions > Generation = 0, Consumption = 0 6 kg/s – 3 kg/s = dn/dt dn/dt = 3 kg/s c) t = 333 s Question 2 (30%) One thousand kilograms per hour of a mixture containing equal parts by mass of methanol and water is distilled. Product streams leave the top and the bottom of the distillation column. The flow rate of the bottom stream is measured and found to be 673 kg/h, and the overhead stream is analyzed and found to contain 96.0 wt% methanol. a) Draw and label a flowchart of the process and do the degree-of-freedom analysis. b) Calculate the mass and mole fractions of methanol and the molar flow rates of methanol and water in the bottom product stream. c) Suppose the bottom product stream is analyzed and the mole fraction of methanol is found to be significantly higher than the value calculated in part (b). List as many possible reasons for the discrepancy as you can think of. Include in your list possible violations of assumptions made in part (b) Solution 2 c. Analyzer is wrong, flow rates are wrong, impurities in the feed, a reaction is taking place Question 3 (25%) Two aqueous sulfuric acid solutions containing 20.0 wt% H2 SO4 (SG = 1.139) and 60.0 wt% H2 SO4 (SG = 1.498) are mixed to form a 4.00 molar solution (SG = 1.213). (a) Calculate the mass fraction of sulfuric acid in the product solution. (b) Taking 100 kg of the 20% feed solution as a basis, draw and label a flowchart of this process, labeling both masses and volumes, and do the degree-of-freedom analysis. Calculate the feed ratio (liters 20% solution/liter 60% solution). (c) What feed rate of the 60% solution (L/h)would be required to produce 1250kg/h of the product? Solution 3 Question 4 (25%) A sedimentation process is to be used to separate pulverized coal from slate. A suspension of finely divided particles of galena (lead sulfide, SG = 7.44) in water is prepared. The overall specific gravity of the suspension is 1.48. a) Four hundred kilograms of galena and a quantity of water are loaded into a tank and stirred to obtain a uniform suspension with the required specific gravity. Draw and label the flowchart (label both the masses and volumes of the galena and water), do the degree-of-freedom analysis, and calculate how much water (m3) must be fed to the tank. b) A mixture of coal and slate is placed in the suspension. The coal rises to the top and is skimmed off, and the slate sinks. What can you conclude about the specific gravities of coal and slate? c) The separation process works well for several hours, but then a region of clear liquid begins to form at the top of the cloudy suspension and the coal sinks to the bottom of this region, making skimming more difficult. What might be happening to cause this behavior and what corrective action might be taken? Now what can you say about the specific gravity of coal? Solution 4 c. Specific gravity of coal < 1.48 < Specific gravity of slate d. The suspension begins to settle. Stir the suspension. 1.00 < Specific gravity of coal < 1.48
How do I apply to Columbia University Fu Foundation School of Engineering and Applied Science (SEAS)?
Applicants must apply online. Applying online will give you greater control of the application process and will allow us to process your application more efficiently.
There are different application links available, which one should I complete?
If you are applying to the departments of Applied Physics/Applied Mathematics, Biomedical Engineering, Chemical Engineering, Civil Engineering, Earth and Environmental Engineering, Industrial Engineering and Operations Research, Mechanical Engineering, or if you are a Columbia student applying MS Express or to the BS/MS program please apply here.
If you are applying to the departments of, Computer Engineering, Computer Science, or Electrical Engineering please apply here.
Which semesters can I apply for?
Admission is available for spring and/or fall start. Some programs only offer admission in the fall. We do not offer a summer semester. Please check the online application for available terms to your program of interest. You can also refer to the relevant departmental website for information.
I previously applied and was accepted, but did not enroll, can I reuse prior materials to apply again?
It depends on how long ago you applied. If you applied less than a year ago and were accepted, you are eligible to apply again using the reactivation application process. The reactivation process allows you to use prior application materials again.
To apply by reactivation, select the appropriate application for admission, based on the department you are applying to, and choose the reactivation application option.
Applicants previously denied or with a prior incomplete status are not eligible for reactivation.
What is the MS Express Application? Am I eligible to apply?
The MS Express application is strictly for current undergraduate students enrolled at Columbia University, Barnard, General Studies, or young Alumni within three years of graduation who meet certain requirements and are applying to MS programs in engineering.
It is not intended for prospective students from other colleges or universities.
If you are eligible and you want to apply, please check the MS Express website for details. Be sure to speak with a faculty adviser if you are interested in applying to an engineering program outside of your current major to find out about prerequisites you may need to make up. You should visit the department of interest website or contact the department directly if you have program or prerequisite coursework questions. You should contact the Office of Graduate Student Affairs if you have questions about the application process email@example.com.
I am interested in two different programs at SEAS — can I apply to both?
No, you must apply to only one program at a time. Do not apply to more than one program at SEAS for a given term or applications may be invalidated.
I am interested in an on-campus program and Columbia Video Network (CVN) program, can I apply to both?
No, you must apply to only one program at a time either on-campus or through CVN. Do not apply to more than one program at SEAS for a given term or applications may be invalidated.
Can I submit my application first and send supplemental material later when available?
You may submit the online application first and send test scores or recommendation letters after if necessary. All other supplemental material must be submitted together with the online application.
Be advised that, after the priority deadline to apply, Columbia reserves the right to evaluate an application and render a final decision even if all pieces of the application have not been received. Furthermore, once a decision is rendered on an application it may not be evaluated again should new supplemental material be received.
Where do I mail official transcripts?
Copies of your transcripts should be uploaded online. Only doctoral applicants to the Computer Science department need to mail official transcripts at the time of application. All other departments may upload copies of official transcripts to the online application system for review purposes. Our office will require official mailed in transcripts at the point of admission.
GRE and or TOEFL scores should be sent via ETS (www.ets.org) to institutional code 2111 (Department code is NOT required).
For IELTS scores, give the school name and address to the test center and enter your TRF number onto the online application in the space provided.
Can I submit additional materials once my application is under evaluation?
Unfortunately, once you have been notified that your application was sent to the department for evaluation of admission you may not update it. Additional materials sent will not be considered in the decision. Furthermore, an application will not be evaluated a second time should the decision be made prior to receiving additional material.
Please be advised candidates should not submit copies of awards or financial documentation to this office since submission of these extra materials will not enhance chances of being admitted. Documents submitted will not be returned.
Computer Science and Electrical Engineering applicants please login to your application to upload or update supplemental material.
Do all of my application materials need to be submitted online?
Yes, applicants must submit all application requirements online. This includes uploaded copies of official transcripts and recommendations. No exceptions are made to the requirement.
For IELTS give the test center the school name and address and enter your TRF number onto the online application in the space provided.
Office of Graduate Student Affairs
The Fu Foundation School of Engineering and Applied Science
500 West 120th Steet, 530 S.W. Mudd, MC 4708
New York, NY 10027
Do I need a degree in engineering to apply?
Ordinarily, the applicant will have majored in the field in which graduate study is intended. But in certain programs, preparation in a related field of engineering or science is acceptable. The applicant will be admitted only if the undergraduate record shows promise of productive and effective graduate work.
How should I pay the application fee?
The application fee is paid online using a major credit card. No other forms of payment are accepted.
Do you accept international/foreign checks for payment of the application fee?
No, the application fee must be paid using a major credit card via the online application system.
I am having technical problems with the online application system. Who should I contact?
It is best if you locate and contact the webmaster or technical support from your online application. If you continue to have the problem you may email the Office of Graduate Student Affairs at firstname.lastname@example.org and we will contact them for you.
May I provide you with any background information about myself, such as GPA, education/experience, and or test score results to learn about my chances for admission or possibility for financial aid before applying?
Unfortunately, we can not evaluate your candidacy prior to submission of a complete application.
There is no specific cutoff for standardized test scores or GPA.