EXAM I Review Name:________________

SPRING 2006

BAE 3023

Single variable linearization

1. Reaction rates of biological and chemical systems are typically a function of temperature. The Arrhenius equation below is commonly useful to model the temperature effect.

Where k is reaction rate (Kg moles s^-1)

A is a rate constant (Kg moles s^-1)

Ea is activation energy (kJ mol^-1)

T is absolute temperature (⁰K)

R is the ideal gas constant (kJ mol^{-1 0}K^{-1 )}

Determine a linear form of the equation about an operating temperature, T₀ , relating reaction rate (k) to temperature (T).

System modeling

2. Derive a transfer function for the following system relating inlet to outlet concentration. Make and document the necessary assumptions. Assume q₁,q₂ and C₂ are constant and that q has units of [m³/s] and C units of kg/m³.

System identification for first order systems

3. A step test was performed to determine the response characteristics of a pH probe. The following chart resulted as a response to a change in pH of the measured solution of –2 initiated at 22 sec from the start of the chart. Propose a differential equation that could be used to describe the dynamic characteristics of the probe. If the probe were exposed to a sinusoidally varying pH with a magnitude of 1 pH at 0.5 rad/s, what would the frequency of the response be?

Solutions of DE’s by LaPlace Transform technique

Will the response c(t) of the system described by the following differential equation be oscillatory for a step in y(t)?

, x(0) = x’(0)=0