Consider a first-order reaction in a ctsr the governing

Question

Question 1 - Consider a first-order reaction in a CTSR. The governing equations, derived from the mass and energy balance, are given by

V dC/dt = F(C₀ - C) - K V C

V ρ dT/dt = FρC_p(T₀ - T) - UA(T - T_j) - ΔHVkC

The rate constant is given by Arrhenius law: 

The constants are given below:

F=1; V=5*10; C₀ = 2; R = 1.987; E_a = 30X10³; k₀ = 2.6X10²⁰;

rho*C_p = 2.5; T₀ = 290; T_j = 278; U*A=10; ΔH = - 20

Use Euler's method with the initial conditions

C(0) = 4*10  and  T(0) = 0  to approximate C(9)

{Hint: First convert into matrix form then apply Euler's method (see slide 12 in section 25.1)}

Question 2 - In the first problem, use Euler's Method to solve the problem for the time period 0 ≤ t ≤. Then plot C(t) and T(t) in separate figures then, Attach the pdf file using MATLAB Publish.

Question 3 - 1) Consider a first-order reaction in a CTSR. The governing equations, derived from the mass and energy balance, are given by

V dC/dt = F (C₀ - C) - kVC

V ρ dT/dt = FρC_p(T₀ - T) - UA(T - T_j) - ΔHVkC

The rate constant is given by Arrhenius law: 

The constants are given below:

F = 1; V = 50; C₀ = 2; R = 1.987; E_a = 30X10³; k₀ = 2.6X10²⁰;

rho*C_p = 2.5; T₀ = 290; T_j = 278; U*A=10; ΔH = -20; 

the initial conditions: C(0) = 10  and  T(0) = 0.

Find the time t so that dC/dt = 1.

Question 4 - 1) Consider a first-order reaction in a CTSR. The governing equations, derived from the mass and energy balance, are given by

V dC/dt = F(C₀ - C) - kVC

V ρ dT/dt = FρC_p(T₀ - T) - UA(T - T_j) - ΔHVkC

The rate constant is given by Arrhenius law: 

The constants are given below:

F = 1; V = 50; C₀ = 2; R = 1.987; E_a = 30X10³; k₀ = 2.6X10²⁰;

rho*C_p = 2.5; T₀  = 290; T_j = 278; U*A=10; Δ H = -20;

the initial conditions: C(0) = 10  and T(0) = 0.

Find the time 0 ≤ t ≤ 10 so that d²T/dt² = 10(d²C/dt²).