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 
3.1 Select the fundamental balances used in chapter 3. 
Fundamental Balances 
Balances involve entities that we believe are conserved! 
3.2 Which ONE of these is not a constitutive model. 
Fundamental Balances 
Heat Transfer
Q = hA(DT) 
Chemical Reaction Rate
r_{a} = k_{0}e^{E/RT}C_{A} 
Degrees of Freedom
DOF = NV  NE 
Phase Equilibrium
y_{i} =K_{i}x_{i} 
Equations of State
PV = nRT 
Fluid Flow
F = C_{v}(DP/r)^{1/2} 
3.3 Select which answer better describes the key differences between fundamental and constitutive models. 

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, 
3.4 If a modelling goal were to determine the time constant and the steadystate gain, which of the following would be the most important subgoal? 

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

3.6 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. 

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

A  Y_{k} = Y_{k1} + (dY/dt)_{k1}Dt 
B  Y_{k} = Y_{k1} + (dY/dt)^{2}_{k1}Dt 
C  Y_{k} = Y_{k1} + (dY/dt)_{k1}(X_{in})_{k1}Dt 
D  Y_{k} = Y_{k1} + K_{p}(1e^{t/t})Dt 