_______________________ Last Name, First CHE426: Problem set #3 (Need to show all the works. Except for plot or numerical calculation, Matlab solutions are not acceptable) 1. An isothermal, first-order, irreversible reaction A B with rate constant takes place in the k liquid phase in a constant-volume reactor. Due to imperfect mixing, the reactor system can be modeled as a two-tank system with back mixing as shown in the sketch below3. Assuming and are constant, write the differential equations describing the F FR concentration and as function of time. Do not solve the equations. CA1 CA1 2. If a forcing function has the Laplace transform f(t) = + f(s) Plot for 0 5. f(t) t 3. Solve the following equation for y(t) 2 = + 3y = 1 y(0) 4. Express the function given in Fig. 3-4 in the and the t-domain s-domain Figure 3-4 5. Sketch the following functions: a) = 2u(t 1) + 3) f(t) u(t) u(t b) = 3tu(t) 3u(t 1) 2) f(t) u(t Determine at = 1.5 and at = 3 for the following function: 6. f(t) t t = 0.5 0.5 1) + (t 3) 2) f(t) u(t) u(t u(t − 7. Find the solution to the following differential equations using Laplace Transforms. + = = a) (t) , 0 y′ y y(0) b) = (t = 0 y′+ y y(0) −1), For the following transforms, find 8. f(t).
_______________________ Last Name, First CHE426: Problem set #3 (Need to show all the works. Except for plot or numerical calculation, Matlab solutions are not acceptable) 1. An isothermal, first-order, irreversible reaction A B with rate constant k takes place in the liquid phase in a constant-volume reactor. Due to imperfect mixing, the reactor system can be modeled as a two-tank system with back mixing as shown in the sketch below3. Assuming F and FR are constant, write the differential equations describing the concentration CA1 and CA1 as function of time. Do not solve the equations. 2. If a forcing function f(t) has the Laplace transform f(s) = + Plot f(t) for 0 t 5. 3. Solve the following equation for y(t) 2 = + 3y y(0) = 1 4. Express the function given in Fig. 3-4 in the t-domain and the s-domain Figure 3-4 5. Sketch the following functions: a) f(t) = u(t) 2u(t 1) + u(t 3) b) f(t) = 3tu(t) 3u(t 1) u(t 2) 6. Determine f(t) at t = 1.5 and at t = 3 for the following function: f(t) = 0.5 u(t) − 0.5 u(t 1) + (t 3) u(t 2) 7. Find the solution to the following differential equations using Laplace Transforms. a) y′ + y = (t) , y(0) = 0 b) y′+ y = (t −1), y(0) = 0 8. For the following transforms, find f(t).
Set3_10.docx