Chapter 6.1, Problem 40E

The van der Waal's equation of state is given as RT a v-b v² For sulfur dioxide at temperature, T, of 300 K and a pressure, P, of 1 atm, the constants are given as: R = 0.08206 L.atm/(mol.K) L2.mol² P = a = 6.7689 atm.L b=0.05679 L.mol™¹ a) Plot the function f(v)=0 the for volumes for the range of 0 to 40 L/mol using 0.5 increment. b) Identify the root in this plot (where the curve crosses x-axis). c) Use the MATLAB function (fzero) to solve the original f(v) function for the specific volume using the initial guess from part (c). d) Use the MATLAB function (roots) to solve the original f(v) function for the specific volume.

A window is in the form of an equilateral triangle surmounted on a rectangle. The rectangle is of clear glass and transmit twice as much light as does the triangle which is made of stained glass. If the entire window has a perimeter of 20 feet, find the dimensions of the window that will admit the most light.

The electric flux density D at the point M (0,4,0) in the region about a uniform line charge of 1 nC/m lying along the z axis in free space is: Select one: a. None of the above b. 0.6366 nC/m c. 0.2387 nC/m d. 0.039 nC/m e. 0.1 nC/m

standard science experiment is to drop a ball and see how high it bounces. Once the “bounciness” of the ball has been determined, the ratio gives a bounciness index. For example, if a ball dropped from a height of 10 feet bounces 6 feet high, the index is 0.6, and the total distance traveled by the ball is 16 feet after one bounce. If the ball were to continue bouncing, the distance after two bounces would be 10 ft + 6 ft +6 ft + 3.6 ft = 25.6 ft. Note that the distance traveled for each successive bounce is the distance to the floor plus 0.6 of that distance as the ball comes back up. Write a program that lets the user enter the initial height from which the ball is dropped, the bounciness index, and the number of times the ball is allowed to continue bouncing. Output should be the total distance traveled by the ball.

A discharge factor is a ratio which compares the mass flow rate at the end of a channel or nozzle to an ideal channel or nozzle. The discharge factor for flow through an open channel of parabolic cross-section is: K = 1.2 [V16x +1+ In(V16x² +1+4x)]³ 4x where x is the ratio of the maximum water depth to breadth of the channel at the top of the water. Determine the discharge factors for x in the range 0.45 to 0.90 in steps of 0.05. Script e C Reset I MATLAB Docume 1 %Give values for x: 2 3 %Solve for K: 4

A rectangle has a perimeter of 20. If the area of the rectangle is to be maximized, the length of each side should be 5

The voltage V(1) (in V) and the current i(t) (in Amp) t seconds after closing the switch in the circuit shown are given by: R Vdt) = V(1– e/) i(t) = e, where t, = RC is the time constant. Consider the case where V = 24 V, R = 3800 2 and C = 4000 x 10-6 F. Determine the voltage and the current during the first 20 s after the switch is closed. Create a vector with values of times from 0 to 20 s with spacing of 2 s, and use it for calculating V(1) and i(t). Display the results in a three-column table where the values of time. voltage and current are displayed in the first, second, and third columns, respectively. (To display values in a Table, just create matrix and have its output displayed) Script ® C Reset I MATLAB Documentation 1 %Don't change the variable name 2 table =

1, t>0 10, t<0 Let u(t) The total energy E of the function x(t) = sin(3t)u(t), is O Eo = 0 O E = 00 O Ex = 0.5 O E = 0.25

FIND THE FOLLOWING: e. time constant f. rise time g. settling time