Podcast
Questions and Answers
Which of the following best describes the relationship between Rizal and Paciano?
Which of the following best describes the relationship between Rizal and Paciano?
- Close friends, with Paciano supporting Rizal financially. (correct)
- Mentors, with Rizal tutoring Paciano in various subjects.
- Distant acquaintances due to differing political views.
- Rivals in academics and leadership.
What was the primary reason Rizal wanted to return to the Philippines in 1887?
What was the primary reason Rizal wanted to return to the Philippines in 1887?
- To practice medicine and establish a clinic.
- To permanently settle and retire from his studies.
- To operate on his mother's eyes. (correct)
- To escape the rising tensions in Europe.
How did Governor-General Emilio Terrero react upon learning about Noli Me Tangere?
How did Governor-General Emilio Terrero react upon learning about Noli Me Tangere?
- He dismissed it as harmless and took no action.
- He summoned Rizal to Malacañang and assigned Don Luis de Andrade as Rizal's bodyguard. (correct)
- He publicly praised the novel for its accurate portrayal of Philippine society.
- He immediately banned the book and ordered Rizal's arrest.
Why did Rizal find Japan more appealing compared to Paris, despite its unique attractions?
Why did Rizal find Japan more appealing compared to Paris, despite its unique attractions?
What was the purpose of Asociacion La Solidaridad, which was founded by Graciano Lopez Jaena?
What was the purpose of Asociacion La Solidaridad, which was founded by Graciano Lopez Jaena?
Which of the following describes the central theme or purpose of El Filibusterismo?
Which of the following describes the central theme or purpose of El Filibusterismo?
Upon arriving in Dapitan after being exiled, what actions did Rizal undertake to improve the community?
Upon arriving in Dapitan after being exiled, what actions did Rizal undertake to improve the community?
What inspired Rizal to write the poem Mi Primera Inspiracion?
What inspired Rizal to write the poem Mi Primera Inspiracion?
During Rizal's time as a student in Ateneo, what distinguished Roman Empire boarders (internos) from the Carthaginian Empire (externos)?
During Rizal's time as a student in Ateneo, what distinguished Roman Empire boarders (internos) from the Carthaginian Empire (externos)?
How did Rizal demonstrate exceptional talent and intelligence at a young age?
How did Rizal demonstrate exceptional talent and intelligence at a young age?
Flashcards
Elias at Salome
Elias at Salome
A chapter in Noli Me Tangere that was deleted.
Dedication
Dedication
Rizal dedicated Noli Me Tangere to his fatherland.
Noli Chapters
Noli Chapters
Noli Me Tangere has 63 chapters plus an epilogue.
Maria Clara Inspiration
Maria Clara Inspiration
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Paciano Helps Rizal
Paciano Helps Rizal
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Tererro's Advice
Tererro's Advice
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Rizal Loves Japan
Rizal Loves Japan
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El Fili Dedication
El Fili Dedication
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Mi Ultimo Adios
Mi Ultimo Adios
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Rizal's Execution
Rizal's Execution
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Study Notes
Chemical Engineering Definitions
- Chemical engineering involves the design, building, and running of industrial chemical plants
- A chemical process is a series of actions that lead to physical, chemical, or bio changes that convert raw materials into products
- Unit operations are fundamental steps in a chemical process involving physical changes like distillation and filtration
- Unit processes are fundamental steps in a chemical process involving chemical reactions such as oxidation and polymerization
Chemical Process Design
- Block Flow Diagrams represent a chemical process, showing unit operations as blocks connected by flow lines
- Process Flow Diagrams build on block flow diagrams with major equipment, flow streams, and control loops shown
- Piping and Instrumentation Diagrams provide a detailed view of all equipment, piping, instrumentation, and control systems in a chemical process
Chemical Process Calculations
- Stoichiometry involves calculating reactant and product quantities in a balanced chemical reaction
- Material Balance applies mass conservation to a chemical process, ensuring mass in equals mass out
- Energy Balance uses energy conservation to track energy inputs, outputs, and transformations within a chemical process
Chemical Reaction Engineering
- Reaction Rate describes how quickly reactants convert to products, typically in concentration per unit time
- Rate Law is an equation expressing reaction rate as a function of reactant and product concentrations
- Batch Reactors mix reactants in a closed system for a set time
- Continuous Stirred-Tank Reactors (CSTR) continuously add reactants and remove products, maintaining constant mixing
- Plug Flow Reactors (PFR) are tubular reactors that ensure reactants flow unidirectionally without mixing back
Thermodynamics
- The First Law of Thermodynamics: Energy is conserved
- The Second Law of Thermodynamics: Entropy in a closed system increases or stays constant
- The Third Law of Thermodynamics: A perfect crystal's entropy is zero at absolute zero
- The Ideal Gas Law: PV = nRT dictates the behavior of ideal gases
- The Van der Waals Equation: (P + a(n/V)^2)(V - nb) = nRT corrects the Ideal Gas Law for real gas behavior
Transport Phenomena
- Fluid Mechanics studies fluid behavior, vital for designing piping and mixing systems
- Viscosity measures a fluid's resistance to flow
- The Reynolds Number, $Re = \frac{\rho v D}{\mu}$, classifies flow as laminar or turbulent
- Bernoulli's Equation describes energy conservation in fluid flow
- Heat Transfer consists of conduction (through solids), convection (via fluid motion), and radiation (through electromagnetic waves)
- Heat Exchangers transfer heat between fluids without mixing
- Mass Transfer: Diffusion moves substances down concentration gradients
- Mass Transfer Coefficient quantifies mass transfer rates between phases
- Distillation separates components via boiling point differences
- Absorption dissolves a gas into a liquid
Chemical Kinetics
- Reaction Rate = $-\frac{d[A]}{dt} = -\frac{d[B]}{dt} = \frac{d[C]}{dt} = \frac{d[D]}{dt}$ for $A + B \rightarrow C + D$
- Rate Law for $aA + bB \rightarrow cC + dD$ is $Rate = k[A]^x[B]^y$
- Zero Order Rate Law: $Rate = k$, $[A] = [A]0 - kt$, $t{1/2} = \frac{[A]_0}{2k}$
- First Order Rate Law: $Rate = k[A]$, $ln[A] = ln[A]0 - kt$, $t{1/2} = \frac{0.693}{k}$
- Second Order Rate Law: $Rate = k[A]^2$, $\frac{1}{[A]} = \frac{1}{[A]0} + kt$, $t{1/2} = \frac{1}{k[A]_0}$
Arrhenius Equation
- $k = Ae^{-E_a/RT}$ defines how temperature affects reaction rate
- $ln(k) = ln(A) - \frac{E_a}{RT}$ illustrates a log-linear relationship
- $ln(\frac{k_2}{k_1}) = \frac{E_a}{R}(\frac{1}{T_1} - \frac{1}{T_2})$ helps compare rates at different temperatures
Reaction Mechanisms
- Elementary steps show single molecular events with direct rate laws, like $Rate = k[A][B]$ for $A + B \rightarrow C$
- A Rate Determining Step is the slowest step that limits the overall reaction rate
Catalysis
- Catalysts accelerate reactions without being consumed
- Homogeneous Catalysts exist in the same phase as reactants
- Heterogeneous Catalysts exist in a different phase than reactants
Radiative Processes - Thomson Scattering
- Differential cross-section: $\frac{d \sigma}{d \Omega}=r_{0}^{2} \frac{1}{2}\left(1+\cos ^{2} \theta\right)$, where $r_{0}=\frac{e^{2}}{m c^{2}}$
- Total cross-section: $\sigma=\frac{8 \pi}{3} r_{0}^{2}=0.665 \times 10^{-24} \mathrm{~cm}^{2}$
Radiative Processes - Thermal Emission
- Emission coefficient $j_{\nu}$ represents energy emitted per volume, time, solid angle, and frequency
- Absorption coefficient $\alpha_{\nu}$ represents the fraction of incident intensity absorbed per unit length
- Kirchoff's Law: $j_{\nu}=\alpha_{\nu} B_{\nu}(T)$, relates emission and absorption to the Planck function
Radiative Processes - Bremsstrahlung Emission
- Emission coefficient: $\epsilon_{\nu}^{f f}=6.8 \times 10^{-38} Z^{2} n_{e} n_{i} T^{-1 / 2} e^{-\frac{h \nu}{k T}} \bar{g}_{f f} \operatorname{erg~cm}^{-3} \mathrm{~s}^{-1} \mathrm{~Hz}^{-1}$
- Electron density is $n_e$, Ion density is $n_i$, Gaunt factor is $\bar{g}_{ff}$, Atomic number is $Z$
Radiative Processes - Bremsstrahlung Absorption
- Absorption coefficient: $\alpha_{\nu}^{f f} \approx 3.7 \times 10^{8} T^{-1 / 2} Z^{2} n_{e} n_{i} \nu^{-3}\left(1-e^{-\frac{h \nu}{k T}}\right) \bar{g}_{f f} \mathrm{~cm}^{-1}$
Algorithmic Analysis
- Divide and conquer:
- A design paradigm where a problem is recursively broken down into smaller subproblems until they are simple enough to solve directly
- Solutions to the subproblems are then combined to solve the original problem
- Divide: Divide the problem into smaller subproblems
- Conquer: Solve the subproblems recursively or directly if they are small enough
- Combine: Combine the solutions of the subproblems
Algorithmic Analysis - Merge sort
- A divide and conquer sorting algorithm
- Splits a list into sublists until each contains one element
- Repeatedly merges the sublists into sorted new lists until there is a single sorted list
Algorithmic Analysis - Binary Search
- An efficient search algorithm for finding the position of a target value within a sorted array
- Compares the target value to the middle element of the array
- If not equal, the half in which the target cannot lie is eliminated, and the search continues on the remaining half
Algorithmic Analysis - Dynamic Programming
- Is a technique for solving complex problems by breaking them down into simpler subproblems, solving each just once, and storing their solutins
- Optimal substructure: A problem exhibits optimal substructure if an optimal solution to the problem contains optimal solutions to the subproblems
- Overlapping subproblems: A problem has overlapping subproblems if the subproblem space is small, meaning the same subproblem is encountered multiple times
Algorithmic Analysis - Fibonacci Sequence
- Recursice: inefficient
- Top-down (Memoization): Starts by resolving the original problem be breaking in into subproblems
- Bottom-up (Tabulation): Starts by solving the smallest uproblems and then uses those solutions to solve larger subproblems
What is Inflation?
- Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, purchasing power is falling
- Central banks attempt to limit inflation and avoid deflation to keep the economy running smoothly
Measuring Inflation
- Inflation is typically measured by the Consumer Price Index (CPI), which tracks the prices of a basket of goods and services purchased by households
Types of Inflation
- Demand-Pull Inflation: Occurs when there is an increase in aggregate demand, leading to a rise in prices
- Cost-Push Inflation: Happens when the cost of production increases (e.g., wages, raw materials), leading firms to raise prices
- Built-In Inflation: Occurs when wages and prices increase in tandem due to expectation of future inflation
Deflation
- A decrease in the general price level of goods and services
- The opposite of inflation
Static Electricity - Charging by Friction
- When 2 neutral objects are rubbed together, electrons can be transferred from one object
- One object ends up with an excess of electrons and becomes negatively charged
- Other object becomes positively charged
Static Electricity - Charging by Conduction
- Charging a neutra object by touching it with a charged objects is called charging by conduction
- When a negatively charged rod touches a neutral object, electrons flow from the rod to the neutral object
- When a positively charged rod touches a netrual object, electrons flow from the object to the rod
Static Electricity - Electric Force
- F is the electric force
- $k = 8.99 \times 10^9 Nm^2/C^2$ is Coulomb's constant
- q1 & q2 are the magnitudes of the charges
- r is the distance between the charges
Static Electricity - Electric Field
- E is the electric field
- F is the electric force
- q is the charge
Oscillations - Simple harmonic motion (SHM)
- Requires a stable equilibrium, restoring force proportional to displacement, and negligible friction
- The spring-mass system exhibits a Hooke’s Law force: F = -kx
- Period: The period $T$ (time for one complete oscillation) is related to $\omega$ by: $T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{m}{k}}$
- Maximum Velocity: The maximum velocity $v_{max}$ is: $v_{max} = A\omega$
- The potential energy $U$ stored in the spring is: $U = \frac{1}{2}kx^2 = \frac{1}{2}kA^2\cos^2(\omega t + \phi)$
Oscillations - Simple Pendulum
- The period is: $T = 2\pi\sqrt{\frac{L}{g}}$
- In a horizontal SHM, angular frequency $\omega = \sqrt{\frac{k}{m}}$
Matrices - Basic Concepts
- Definition: A matrix is a rectangular array of numbers or symbols arranged in rows and columns
- Notation - Matrices are denoted by uppercase letters: e.g., A, B, C.
- Elements are denoted by lowercase letters with subscripts indicating the row and column: e.g., 𝑎𝑖𝑗 is the element in the 𝑖 -th row and 𝑗 -th column
Matrices - Types of Matrices
- Square Matrix: A matrix with an equal number of rows and columns (𝑚=𝑛).
- Row Matrix: A matrix with only one row (1×𝑛).
- Column Matrix: A matrix with only one column (𝑚×1).
- Zero Matrix: A matrix in which all elements are zero.
Matrices - Types of Matrices -Identity Matrix
- Square matrix with ones on the main diagonal and zeros elsewhere
- Denoted by I
Matrices - Types of Matrices - Diagonal Matrix
- A square matrix in which all non-diagonal elements are zero
Matrices - Matrix Operations - Addition
- Matrices can be added if they have the same dimensions. The sum of two matrices A and B is obtained by adding corresonding elements:
- (𝐴+𝐵)𝑖𝑗=𝑎𝑖𝑗+𝑏𝑖𝑗
Matrices - Matrix Operations - Subtraction
- Similar to addition, matrices can be subtracted if they have the same dimensions:
- (𝐴−𝐵)𝑖𝑗=𝑎𝑖𝑗−𝑏𝑖𝑗
Matrices - Matrix Operations - Scalar Multiplication
- Multiplying a matrix by a scalar involves multiplying each element of the matrix by the scalar:
- (𝑘𝐴)𝑖𝑗=𝑘⋅𝑎𝑖𝑗
Mathematics - Tranpose of a Matrix
- The transpose of a matrix A, denoted by 𝐴𝑇, is obrain by interchanging its rows and columns.
Physics - Kinematics - definitions
- Displacement: the change in position of an object * Denoted as $\Delta x$ * $\Delta x = x_{f} - x_{i}$
- Velocity: The rate of change of displacement * $v = \frac{\Delta x}{\Delta t}$ * Units: 𝑚/s
- Acceleration: The rate of change of Velocity * $a = \frac{\Delta v}{\Delta t}$ * Units: 𝑚/s2
Physics - Dynamics - Newton's Laws of Motion - 1st law
- An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force
Mathematics - Physics - Dynamics
- Forces * Gravity * $F=mg22.14$ * Friction * Static: $F_{s} \leq \m_{s}N$ * Kinetic: $F_{k} = \m_{k}N$
Physics - Work and Energy - Definitions
- Work: the energy transferred to or from an pbject by means of a force acting on the object * $W = Fdcos\theta$ * Units: Joules (J)
- Kinetic Energy: The energy of motion * $KE = \frac{1}{2}mv^{2}$ * Units: Joules (J)
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