Develop mass balance equations for the reactors

Assignment Help Engineering Mathematics
Reference no: EM131069995

1. Figure P1 shows three chemical reactors linked by pipes. As indicated, the rate of transfer of chemicals through each pipe is equal to a flow rate (Q, with units of cubic meters per second) multiplied by the concentration of the reactor from which the pipe originates (c, with units of milligrams per cubic meter). If the system is at a steady state, the transfer into each reactor will balance the transfer out. Develop mass balance equations for the reactors, and use Gaussian elimination to solve the three simultaneous linear algebraic equations for the unknown concentrations c1, c2, and c3.

428_Figure.png

2. Let

880_Figure1.png

(a) Find the condition that α, β, and γ must satisfy so that det P = det Q.

(b) Find Q-1 in terms of α, β, and γ. State the condition for which Q-1 exists.

3. Suppose

455_Figure2.png

where a and b are arbitrary real numbers. Find the values of a and b, if any, such that

(a) b is not in the column space of A;

(b) the nullity of A is equal to 1;

(c) the nullity of A is equal to 2.

4. Let the linear transformation f : R3 |→ R3 be defined by

f(1, 0, 0) = (1, 0, 0),          f(1, 1, 0) = (0, 1, 0),         and        f(1, 1, 1) = (0, 0, 1).

(a) Find the matrix representation of f with respect to the standard basis in R3.

(b) Find f(1, 2, 3).

(c) Find all vectors v = [x y z]T in R3 such that f(x, y, z) = (0, 0, 0).

5. Consider the following 4 × 4 matrix

2482_Figure3.png

In MATLAB you would obtain this matrix as eye(4) - ones(4).

(a) Find all the eigenvalues of A, including multiplicities.

(b) For each of the eigenvalues you found in part (a), find a corresponding set of eigenvectors.

(c) Is A diagonalizable? Why or why not? Provide a complete explanation.

Reference no: EM131069995

Questions Cloud

Calculate the precise resonant frequency : Determine the lower critical frequeircy and label this poirrt otl your graph. Determine the upper critical frequency and label this point on your graph.
What is deferred tax : What is deferred tax? And how does it affects financial Statements. Kindly provide an detailed explanation for full credits.
Ratio analysis for government financial condition analysis : 1. What general problems must be addressed in doing ratio analysis for government financial condition analysis? 2. Do traditional solvency ratios adequately address financial condition analysis concerns?
Production capital-intensive or labor-intensive : In which of the four market structures does each firm operate? Describe the attributes of the firm's market that show why that is the relevant market structure.
Develop mass balance equations for the reactors : If the system is at a steady state, the transfer into each reactor will balance the transfer out. Develop mass balance equations for the reactors, and use Gaussian elimination to solve the three simultaneous linear algebraic equations for the unkn..
The values of mt are computed by invoking the principle : Taylor-type calculations are not possible for HCP polycrystals where twinning and nonbasal slip influence deformation.
Machine now versus leaving the account untouched : The machine costs $200. How much less will the account be worth in 8 years if she buys the karaoke machine now versus leaving the account untouched?
Differentiating factor between revenues and earnings : What is the main differentiating factor between revenues and earnings?
Normal recovery period : Under MACRS, an asset which originally cost $100,000 is being depreciated using a 10-year normal recovery period. The depreciation expense in year 5 is ________.

Reviews

Write a Review

 

Engineering Mathematics Questions & Answers

  A standard normal probabilities based problems

Are the results enough evidence to conclude that the bottles are not filled adequately at the labeled amount of 6 ounces per bottle?

  Problem regarding the maximize the return on investment

If he decides that his investment in the stock of company A is to exceed his investment in the stock in company B by at least $20,000, determine how much he should invest in the stock of each company in order to maximize the return on his investme..

  Two linear regression and multiple regression

Does it appear that gender/sex is a significant factor in the differences in salary in this sample?

  Find the equation of the tangent line

Find the equation of the tangent line to the graph and Find the velocity and the acceleration of the particle and position of a particle moving along a straight line

  Natural law school of jurisprudence

Which of the following is most consistent with the Natural Law School of jurisprudence?

  1 every convergent sequence contains either an increasing

1 every convergent sequence contains either an increasing or a decreasing subsequence.?proof suppose that limas n goes

  What are the fin efficiency and effectiveness

What are the fin efficiency and effectiveness? If there are 125 such fins per meter of tube length what is the rate of heat transfer per unit length of tube?

  Comparing the means of two or more groups

The steps in testing a research hypothesis. Comparing the means of two or more groups. Calculating the correlation between two variables

  Determine the floor space

Formulate a linear programming model that can be used to determine the floor space that should be devoted to each department in order to maximize profit contribution.

  Problem regarding the minfly golf company manufactures

Minfly Golf Company manufactures golf balls at Philadelphia, Chicago, and Denver. Cases of golf balls are shipped to warehouses in Orlando, Dallas, and Los Angeles. The following table provides the weekly capacities of the factories and the minimu..

  Write the mathematical formulation of the problem

Describe the components decision variables, the objective function, and the constraints in the context of problem - In this document, write the mathematical formulation of the problem.

  Determine corner points

After the hurricanes in Florida in the summer of 2004, FEMA sent disaster relief trucks to the state carrying bottled water and generators. Each truck could carry no more than 6000 pounds of cargo. Each case of bottled water weighed 25 pounds and ..

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd