The Redlich-Kwong equation of state (RK EOS) is: RT a V-b √TV (V + b) P = where P is the pressure, I the absolute temperature, and R the gas constant. The coefficients a and b are given in terms of Tc and Pc for the fluid, by a = 0.42748R² T 2.5/P and b = 0.08664R Tc/Pc You will find the values of V for which P = 9.46 bar (= 946kPa) at T=350K for n-butane,
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- (Conversion) An object’s polar moment of inertia, J, represents its resistance to twisting. For a cylinder, this moment of inertia is given by this formula: J=mr2/2+m( l 2 +3r 2 )/12misthecylindersmass( kg).listhecylinderslength(m).risthecylindersradius(m). Using this formula, determine the units for the cylinder’s polar moment of inertia.The displacement of an oscillating spring can be described by x = A cos(wt) where x = displacement at time t, A = maximum displacement, w = angular frequency, which depends on the spring constant and the mass attached to the spring, and t = time. Find the displacement, x, with maximum displacement A of 4 cm, for times from 0 to 120 seconds with increments of 30 seconds, and angular frequencies from 0.4 to 0.6 radians/sec, with increments of 0.1 radians/sec. The displacement for all combinations of times and angular frequencies needs to be calculated. Use meshgrid. Display your results in a matrix with angular frequencies along the top row and times along the left column like so (you may put zero, 0, or NaN, in the upper left corner: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.
- Simplify the following Boolean functions, using Karnaugh map:F(A,B,C,D) = ∑(0, 2, 4, 5, 6, 7, 8, 10, 13, 15)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: 4A simple pendulum of length L, has a maximum angular displacement e_max. At one point in its motion, its kinetic energy is K = 3 J and its potential energy is U = 4.2 J. When the pendulum's angular velocity is one-fourth its maximum value (0' = %3D O'_max/4), then its kinetic energy is:
- Two small charged objects attract each other with a force F when separated by a distance d.If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to d/2,the force becomes?Given two particles with Q = 4.30-µC charges as shown in the figure below and a particle with charge q = 1.39 x 10-18 C at the origin. (Note: Assume a reference level of potential V = 0 at r = co.) x = -0.800 m x = 0.800 m (a) What is the net force (in N) exerted by the two 4.30-µC charges on the charge q? (Enter the magnitude.) N (b) What is the electric field (in N/C) at the origin due to the two 4.30-pC particles? (Enter the magnitude.) V N/C (c) What is the electrical potential (in kV) at the origin due to the two 4.30-uC particles? 96.75 V kV (d) What If? What would be the change in electric potential energy (in J) of the system if the charge g were moved a distance d = 0.400 m closer to either of the 4.30-µC particles?An oscillating current in an electric circuit is described by i(t) = 9e cos(2rt) where t is in seconds. Use False Position Method to determine the value of t such that i=3.5. Plot the graph of the function to develop your initial guess. Terminate your computation when the approximate relative error falls below ɛs=10°. Give the results in a table.
- 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 =A simple pendulum is formed of a rope of length L = 2.2 m and a bob of mass m. %3D When the pendulum makes an angle e 10° with the vertical, the speed of the %3D bob is 2 m/s. The angular speed, e', at the lowest position is equal to: (g = 10 m/s^2)20, Solve the equations Ax = b, where