(Solved):   1. A gas laboratory cylinder initially at \( 75 \mathrm{~atm} \) of (absolute) pressure de ...

 

1. A gas laboratory cylinder initially at \( 75 \mathrm{~atm} \) of (absolute) pressure develops a small leak through the regulator. The molar flow rate of gas out of the cylinder is proportional to the square root of the pressure difference between the cylinder and the barometric pressure in Gaziantep which(s \( 0.9 \) atm. After 6 days the pressure in the cylinder is \( 2.5 \) atm of (absolute) pressure. Assuming the gas to be ideal: a) Find the (absolute) pressure in the cylinder as a function of time. (15 \( \mathrm{p} \) ) b) The molar flow rate of the gas through the leak as a function of time. (6 p) c) The pressure after 4 days and the discharge time. (4 p) 2. Using the least squares method, fit the following data to an equation of Arrhenius form: \( k=A \exp \left(-E_{a} / R T\right) \), here \( k \) is the reaction rate constant, \( T \) is the absolute temperature in \( K \) and \( R=8.3 \mathrm{j} / \mathrm{gmol} \).K.(the universal gas constant) In other words, find the values of \( A \) and \( E_{a} \) so that the following data will be represented best by the equation \( k=A \exp \left(-E_{a} / R T\right)(20 \mathrm{p}) \) 3. An evaporator initially contains \( 400 \mathrm{~L} \) of a solution consisting of \( \mathrm{C}_{\mathrm{AD}}=5 \mathrm{~g} \) sugar(A) \( / \mathrm{L} \) solution and \( \mathrm{C}_{80}=10 \mathrm{~g} \) citric acid(B) \( / \mathrm{L} \) solution. There are two feeds entering the evaporator: The first feed consists of \( 10 \mathrm{~g} \mathrm{A/L} \) and \( 2 \mathrm{~g} B / \mathrm{L}_{\text {, with flow rate of } 5 \text { L min }}^{\text {min }} \) and the second feed consists of \( 5 \mathrm{~g} \mathrm{A/L} \) and \( 3 \mathrm{~g} \) B/Lwith flow rate of \( \mathrm{L} / \mathrm{min} \). The concentrated solution leaving the evaporator is \( 4 \mathrm{~L} / \mathrm{min} \) and amount of water evaporated is \( 6 \mathrm{~kg} / \mathrm{min} \). The density of solution of all concentrations is \( 1.1 \mathrm{~kg} / \mathrm{L} \). Assuming perfect stirring: a) Draw the figure for the evaporator and place all data on it ( \( 5 p \) ) b) Determine the concentration of sugar(A), in \( g A / L \), as a function of time(10 p) c) The concentration of citric acid(B), in \( \mathrm{g} B / L \), as a function of time \( (7 \mathrm{p}) \) d) The \( C_{A} / C_{B} \) ratio after 100 minutes ( \( 3 p \) ) 4. A cylindrical steam-jacketed \( \operatorname{tank}(\mathrm{H} / \mathrm{D}=0.80) \) is filled \( 6,800 \mathrm{lb} \) of tomato paste whose initial temperature is \( 50^{\circ} \mathrm{F} \). The tomato paste is well agitated. The heating area is the area which is in contact with tomato paste. The steam in the jacket is condensing at \( 250^{\circ} \mathrm{F} \). The overall heat transfer coefficient between the tomato paste and steam is \( 40 \mathrm{btu} / \mathrm{hr} \). \( { }^{\circ} \mathrm{F} . \mathrm{ft}^{2} \). Heat is lost only from the upper surface of the tank with \( h=20 \) btu/hr. \( { }^{\circ} \mathrm{F} . \mathrm{ft}^{2} \). and \( T_{\mathrm{a}}=32{ }^{\circ} \mathrm{F} \). Assuming \( C_{p}=0.80 \) btu/b. \( { }^{\circ} \mathrm{F} \), and \( \rho=68 . \mathrm{lb} / \mathrm{t}^{3} \) for tomato paste, and \( h_{t_{0}}=950 \mathrm{btu} / \mathrm{b} \) for steam, determine: a) The temperature of the tomato paste as a function of time. \( (10 \mathrm{p}) \) b) The maximum temperature of the tomato paste \( (5 p) \) c) The rate of heat loss from the top surface as a function of time \( (5 p) \) d) The mass of the steam being condensed as a function of time \( (5 p) \) e) The average mass flow rate of steam used to heat the paste to \( 170^{\circ} \mathrm{F} .(5 \mathrm{p}) \)