REACTION ENGINEERING - EXAMPLE 13.3 : The half-life for first order reaction could be described in the differential equation dC / dt = -kC where k is a constant, C is concentration and t is time. (a) Find the equation of C as a function of t. (b) Find the half life for such reaction or the time required to reduce 50 % of the initial concentration, where k = 0.139 per minute. (c) When the initial concentration Co is 16 mol / cubic metre, how long does the reaction required to achieve the final concentration of 1 mol / cubic metre?

BIOPROCESS ENGINEERING - EXAMPLE 14.1 : In differential centrifugation of cells with diameter D in centimeter, the square of D is given by D x D = [18n ln (RF / RI) ] / [ (RP - RFF) Wt ] where n is the fluid viscosity (poise), RF is the final radius of rotation (cm), RI is the initial radius of rotation (cm), RP is cell density (g / ml), RFF is the fluid density (g/ml), W the square for the rotational velocity in (radians / s) (radians / s), t is the time required to sediment from RI to RF (s). Derive an equation for W as a function for D, n, RF, RI, RP, RFF and t, with the stated units above, in radian & degree.

BIOPROCESS ENGINEERING - EXAMPLE 14.2 : An aqueous solution with 2.5 g of a protein dissolved in 600 cubic centimeters of a solution at 20 degree Celsius was placed in a container that has a water-permeable membrane. Water permeated through the membrane until the h - level of the solution was 0.9 cm above the pure water. (a) Calculate the absolute temperature of the solution, T in Kelvin, where T (Kelvin) = T (degree Celsius) + 273.15. (b) Calculate the osmotic pressure, P of the solution by using the formula P = hrg where h is level of the solution, r is density of water with 1000 kg per cubic meter, g = 9.81 N / kg as gravitational acceleration. (c) Calculate the concentration of the protein solution, C in kg / cubic meter. (d) Calculate the molecular weight of the protein, (MW) = CRT / P where R = 8.314 Pa cubic meter / (mol K) as ideal gas constant.

ENGINEERING MECHANIC - EXAMPLE 15.1 : What is the meaning – strain? In a distillation column, if a block 10 cm on a side is deformed so that it becomes 9 cm long, what is the strain involved in percentage?

BIOPROCESS ENGINEERING - EXAMPLE 14.3 : The kinetic behavior of an enzyme could be described using Michalis - Menten equation : Vo = Vmax [S] / (Km + [S]). Derive this equation from [ES] = [E]total [S] / (Km + [S]), Vmax = Kcat [E]total, Vo = Kcat [ES].

ENGINEERING MECHANIC - EXAMPLE 15.2 : A cantilever beam of length L = 3 m carries a uniformly distributed load (UDL) of W = 20 N / m throughout the length. Calculate the bending moment, BM of the beam near the fixed end. What is the shear force, SF at this point? Let SF = -WL, BM = -LWL/2.

ENGINEERING MECHANIC - EXAMPLE 15.3 : A biochemical trolley of mass 15 kg is towing a trailer of mass 5 kg along a straight horizontal pathway. The trailer and the trolley are connected by a light inextensible tow-bar. The engine of the trolley exerts a driving force of magnitude 100 N. The trailer and the trolley experience resistances of magnitude 10 N and 30 N respectively. (a) Form 2 equations with unknowns T and a, that represents the equilibrium for the 2 systems of the trolley and trailer. (b) Solve the simultaneous equations from the 2 equations that are obtained in part (a) of this question. T is the tension of the tow-bar and a is the acceleration.

Question 105 - In a rigid rotor model in quantum chemistry, the moment of inertia I is given by an Equation E as I = Ma x La x La + Mc x Lc x Lc = m x L x L, where m = (Ma x Mc) / (Ma + Mc) and L = La + Lc, m is the reduced mass, Ma is the mass of a, Mc is the mass of c, La is the radius of a from point O, Lc is the radius of c from point O. Prove by simplest method that Equation E is wrong.

ELECTRICAL TECHNOLOGY - EXAMPLE 16.1 : According to Shockley equation, the I - V characteristic of a diode is approximated by I = IS [ exp (nVD / VT) - 1 ]. For silicon, let the reverse bias saturation current IS as 0.000000000001. If n is ideality factor with value of 1.5, VT as thermal voltage drop of 0.026 V at room temperature, what is the value of current I that passes through the silicon diode in the heater of evaporator when the forward voltage drop VD = 0.026 V? Please take note that exp is the exponential function with e(1) = 2.718, e(2) = 7.389.

ELECTRICAL TECHNOLOGY - EXAMPLE 16.2 : In a selection of suitable heating equipment for drying of crystals of biochemical, the one of the lowest current consumption will be chosen for safety consideration. Selection is available : (A) 120 V microwave oven 1800 W. (B) 240 V conventional oven 11000 W. Which one should be chosen and why?

COMPUTER PROGRAMMING FOR ENGINEERS - EXAMPLE 17.1 : By using Excel or other easiest programming package, explain how I, the integral of sin x dx from 0 to 3.142 could be approximated using random number. Find the exact value of I.

ELECTRICAL TECHNOLOGY - EXAMPLE 16.3 : In the design of a solar power system steps of calculations below are followed : (a) The power output of the inverter of the solar panel is 100 watts. What is the power input, Pin to the inverter when the efficiency of the inverter is 50 %? (b) If the rated power of the inverter is 300 watts, how many inverter is needed for the solar panel? (c) Charge controller of V = 12 volts is used to supply power to the inverter. What is the input current I to the inverter? (d) If the charge controller capacity is 10 A, how many charge controllers are needed? (e) If a biochemical mixer consumes 100 watts, running for 2 hours per day, what is the energy consumption in kilowatt hour per day? (f) What is the input energy needed when the efficiency of the inverter is 50 %? (g) If your area receives 2.88 hours of full sunlight per day, how much energy, in kilowatt hour can be produced per day when one solar panel can produce 20 watts of power? (h) If you know that you have to produce total energy as the answer for (f), how many solar panels are needed? (i) Each V = 12 V battery has 5 ampere hours. If the total energy needed is in answer (f), then how many batteries are needed to run the biochemical mixer if without sunlight for 3 days?

Question 104 - In photoelectrical effect analysis of quantum chemistry, let E = kinetic energy of electron, p = intensity of UV light, f = frequency of UV light. According to Classical Theory, E = c for all values of f, E = mp. According to Quantum Theory, E = c for all values of p, E = mf + c. In a graph, m and c are constants where m is slope and c is y intercept. If m = 2 and c = 3 with similar value of E : (a) find the value of p according to Classical Theory; (b) find the value of f according to Quantum Theory.

COMPUTER PROGRAMMING FOR ENGINEERS - EXAMPLE 17.2 : There are 5 simultaneous equations with 5 unknowns as follow : 16 V - 4 X - Z = 36, 4 X - 4 W - Y + Z = 3, 8 V + 4 W - X + Y = 10, X - W = 1, V + W = 0. Find the values of V, W, X, Y and Z accurately within 15 minutes. State the computer program that you use to get the answers.

COMPUTER PROGRAMMING FOR ENGINEERS - EXAMPLE 17.3 : (a) The byte is the basic building block of computer data used in chemical engineering process simulation where 16 bits make a word, 4 bits make a nibble, 32 bits make a quad word and 8 bits make a byte. Then how many nibbles are there in a megabytes? (b) In computer data items, let : 1 bit - counts from 0 to 1, 8 bits - counts from 0 to 255, 16 bits - counts from 0 to A. What is the value of A? (c) In a binary system of 4 bits, if 1100 = 12, 1101 = 13, 1110 = 14, 1111 = 15, B = 16, then guess the value of B. (d) By using any form of tools, find the exact value of 2 power 64 or 2^64.