Chapter 3    Mathematical Modelling Principles
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Check Your Reading             Study Questions             Thought Questions

In this chapter, there were six main concepts.   The questions will be categorized according to the most relevant concept.

Modelling Procedure Fundamental Balances Degrees of Freedom
Linearity Numerical Methods System Insight











Check Your Reading

Solidify the Concepts

Select the
fundamental balances used in chapter 3.

Fundamental Balances

Balances involve entities that we believe are conserved!

Constitutive Balance

Overall Material Balance

Charge Balance

Component Balance

Energy Balance

Triple Beam Balance













Which ONE of these is not a
constitutive model.

Fundamental Balances

Hint: What are the characteristics of constitutive models?



Heat Transfer               Q = hA(DT)

Chemical Reaction Rate       ra = k0e-E/RTCA

Degrees of Freedom      DOF = NV - NE

Phase Equilibrium               yi =Kixi

Equations of State         PV = nRT

Fluid Flow                         F = Cv(DP/r)1/2









Select which answer better describes the key differences between fundamental and constitutive models.

Fundamental Balances




 Fundamental models govern all physical systems under common assumptions valid for chemical processes.

Constitutive equations are valid within the ranges of the underlying data and are often sufficiently accurate for the specific system being studied.

Fundamental models are universally applicable,
and govern all physical systems.

Constitutive equations are absolutely accurate
for a specific problem.
















If a modelling goal were to determine the time constant and the steady-state gain, which of the following would be the most important sub-goal?

Modelling Procedure


To perform the material balance

To linearize around a base point

To apply the appropriate constitutive equations

To perform a degrees of freedom analysis















Select the output response which would result from a single step input to a
first order system.

System Insight






The numerical solution for a differential equation provides the
exact values of the dependent variable for the specified value of the input variable and the specified initial condition.

Numerical Methods

TRUE         FALSE











Which of the following is the correct form of the
Euler integration formula for a first order differential equation?

Numerical Methods




A Yk = Yk-1 + (dY/dt)k-1Dt
B Yk = Yk-1 + (dY/dt)2k-1Dt
C Yk = Yk-1 + (dY/dt)k-1(Xin)k-1Dt
D Yk = Yk-1 + Kp(1-e-t/t)Dt