Thermodynamics: Energy, Systems, and Properties

Energy

• Kinetic Energy (KE) refers to the energy of motion and is expressed as $KE = \frac{1}{2}mv^2$.
• Potential Energy (PE) is the energy of position, where $PE = mgh$.
• Internal Energy (U) pertains to the energy linked to the molecular structure of a system.

Thermodynamic System and Surroundings

• A system is a definite quantity of matter or a specific region in space chosen for study.
• Surroundings include mass or space outside the system.
• The boundary is the surface, real or imagined, that separates the system and its surroundings.

Types of Systems

• An isolated system exchanges neither mass nor energy with its environment.
• A closed system allows energy exchange but not mass exchange with its environment.
• An open system permits the transfer of both mass and energy with its environment.

Properties of a System

• Intensive properties, like temperature, pressure, and density, remain independent of the system size.
• Extensive properties, such as mass, volume, and total energy, depend on the system's size or extent.

Thermodynamic Equilibrium

• Thermodynamic equilibrium means the system maintains thermal, mechanical, phase, and chemical equilibrium.
• Thermal equilibrium: same temperature
• Mechanical equilibrium: same pressure
• Phase equilibrium: mass of each phase remains constant
• Chemical equilibrium: no change in chemical composition

Processes and Cycles

• A process involves any alteration a system undergoes from one equilibrium state to another.
• A cycle describes a series of processes bringing a system back to its initial state.

Types of Processes

• Isothermal: constant temperature.
• Isobaric: constant pressure.
• Isochoric (Isometric): constant volume.
• Adiabatic: No heat transfer.

Heat (Q)

• Heat involves energy transfer due to a temperature difference.
• Units for heat are Joules (J) or British Thermal Units (BTU).
• $Q > 0$ signifies heat added to the system.
• $Q < 0$ indicates heat rejected by the system.

Work (W)

• Work reflects the energy transfer from a force acting over a distance.
• Units: Joules (J) or BTU.
• $W > 0$ represents work done by the system.
• $W < 0$ signifies work done on the system.
• Mechanical Work: $W = \int F , dx$
• Electrical Work: $W = VIt$

Sign Convention

• Heat added to the system is positive.
• Heat rejected by the system is negative.
• Work done by the system is positive.
• Work done on the system is negative.

Modes of Heat Transfer

• Conduction: Heat transfer through a solid or stationary fluid.
• Convection: Heat transfer between a solid surface and a moving fluid.
• Radiation: Heat transfer via electromagnetic waves.

Zeroth Law of Thermodynamics

• States that if two systems are in thermal equilibrium with a third system, they are also in thermal equilibrium with each other.

First Law of Thermodynamics

• Energy cannot be created or destroyed and can only change forms.
• For a closed system: $\Delta U = Q - W$
• $\Delta U$: Change in internal energy.
• $Q$: Heat added to the system.
• $W$: Work done by the system.

Second Law of Thermodynamics

• The total entropy of an isolated system can only increase over time or remain constant in ideal cases where the system is in a steady state or undergoing a reversible process.
• Entropy (S) is a measure of the disorder or randomness of a system.
• $\Delta S \geq 0$ for an isolated system.
• Carnot Efficiency: $\eta_{carnot} = 1 - \frac{T_c}{T_H}$
• $T_c$: Absolute temperature of the cold reservoir.
• $T_H$: Absolute temperature of the hot reservoir.

Third Law of Thermodynamics

• The entropy of a system approaches a minimum or zero value as the temperature approaches absolute zero.

Polytropic Process

• A process following the relationship: $PV^n = \text{constant}$.
• $P$: Pressure
• $V$: Volume
• $n$: Polytropic index

Special cases of Polytropic Process

• $n = 0$: Isobaric process ($P = \text{constant}$).
• $n = 1$: Isothermal process ($PV = \text{constant}$).
• $n = \gamma$: Adiabatic process ($PV^\gamma = \text{constant}$), where $\gamma = \frac{C_p}{C_v}$.
• $n = \infty$: Isochoric process ($V = \text{constant}$).

Reversible and Irreversible Processes

• A reversible process can be reversed without any impact on its surroundings.
• An irreversible process leaves a trace on the surroundings and cannot be reversed completely.

Power Cycles

• Convert added heat into work.
• Examples: Otto, Diesel, Rankine cycles.
• Thermal Efficiency: $\eta_{th} = \frac{W_{net}}{Q_{in}}$
• $W_{net}$: Net work output.
• $Q_{in}$: Heat input.

Refrigeration Cycles

• Transfer heat from a low-temperature region to a high-temperature region.
• Examples: Vapor-compression refrigeration cycle.
• Coefficient of Performance (COP): $COP = \frac{Q_c}{W_{net}}$
• $Q_c$: Heat removed from the cold reservoir.
• $W_{net}$: Net work input.

Heat Pump Cycles

• Used for heating purposes, move heat from a low-temperature region to a high-temperature one.
• $COP = \frac{Q_H}{W_{net}}$
• $Q_H$: Heat delivered to the hot reservoir.
• $W_{net}$: Net work input.

Ideal Gas Equation of State

• Described by the equation: $PV = nRT$
• $P$: Pressure
• $V$: Volume
• $n$: Number of moles
• $R$: Ideal gas constant
• $T$: Temperature

Specific Heats

• $C_v$: Specific heat at constant volume.
• $C_p$: Specific heat at constant pressure.
• $C_p - C_v = R$
• Radio of specific heats: $\gamma = \frac{C_p}{C_v}$

Internal Energy and Enthalpy Changes

• $\Delta U = mC_v\Delta T$
• $\Delta H = mC_p\Delta T$

Compressibility Factor

• $Z = \frac{PV}{RT}$
• For ideal gases, $Z = 1$.
• For real gases, $Z \neq 1$.

Van der Waals Equation of State

• Describes real gases: $(P + \frac{a}{v^2})(v - b) = RT$
• Where $a$ and $b$ are constants specific to each gas.
• $v$: Specific volume

Dalton's Law of Partial Pressures

• States that in a mixture of gases, the total pressure equals the sum of the individual partial pressures.
• $P_{total} = P_1 + P_2 +... + P_n$

Amagat's Law of Additive Volumes

• Declares that the total volume in a gas mixture is the sum of each gas's individual partial volumes.
• $V_{total} = V_1 + V_2 +... + V_n$

Mole Fraction

• Proportion is shown with equation.
• $y_i = \frac{n_i}{n_{total}}$
• $n_i$: Number of moles of component $i$.
• $n_{total}$: Total number of moles in the mixture.

Psychrometry-Definitions

• Dry-bulb temperature (Tdb): Is measured with a freely exposed thermometer.
• Wet-bulb temperature (Twb): Results from the temperature a volume of air has if cooled adiabatically to saturation.
• Dew-point temperature (Tdp): Is the temperature a volume of air has if cooled to saturation.
• Relative humidity (RH): Depicts the ratio of moisture in the air versus moisture content at saturation.
• $RH = \frac{P_v}{P_g}$
• $P_v$ : Partial pressure of water vapor
• $P_g$ : Saturation pressure of water vapor at the dry-bulb temperature
• Humidity ratio (ω): Mass of water vapor per unit mass of dry air.
  • $\omega = 0.622 \frac{P_v}{P - P_v}$
  • $P$: Total pressure of the air

Psychrometric Chart

• A graphical representation of the thermodynamic properties of moist air.
• Used to determine various air properties such as humidity ratio, relative humidity, enthalpy, and specific volume.

Psychrometric Processes

• Heating: Increasing the dry-bulb temperature.
• Cooling: Decreasing the dry-bulb temperature.
• Humidification: Increasing the humidity ratio.
• Dehumidification: Decreasing the humidity ratio.
• Adiabatic Mixing: Mixing of two air streams without heat transfer.

Hormones

• A regulatory chemical secreted into extracellular fluid, transported by blood, and acting on target cells.

Types of Signaling

• Endocrine: Hormone secretion affects distant target cells.
• Paracrine: Affects nearby target cells.
• Autocrine: Affects the secreting cell itself.
• Synaptic: Neurotransmitters affect postsynaptic cells.
• Neuroendocrine: Neurohormones diffuse into the bloodstream

Classes of Hormones

• Water-Soluble: Polypeptides, proteins, amines.
  • Secreted by exocytosis.
  • Travel freely in the bloodstream.
  • Bind to cell-surface receptors.
• Lipid-Soluble: Steroids.
  • Diffuse across cell membranes.
  • Travel in the bloodstream bound to transport proteins.
  • Diffuse through the cell membrane and bind to receptors.

Hormone-Receptor Binding

• Initiates a signal transduction pathway.
• Leads to changes in gene transcription and cytoplasmic function.

Example: Epinephrine

• Liver cells: triggers the release of glucose
• Blood vessels of skeletal muscle: vasodilation
• Blood vessels of intestines: vasoconstriction

Endocrine Glands

• Hypothalamus
• Pineal gland
• Pituitary gland
• Thyroid gland
• Parathyroid glands
• Adrenal glands
• Pancreas
• Ovaries (in females)
• Testes (in males)

Control Pathways

• Hormones are assembled into control pathways.
• Hormone release is often controlled by negative feedback.
• The hypothalamus integrates endocrine and nervous systems.

Hypothalamus and Pituitary

• Hypothalamus controls the pituitary gland.
• Posterior Pituitary: Stores and secretes hormones synthesized by the hypothalamus.
  • Antidiuretic hormone (ADH): Promotes water retention by the kidneys.
  • Oxytocin: Stimulates uterine contractions and milk ejection.
• Anterior Pituitary: Produces and secretes hormones that control other endocrine glands.
  • Growth hormone (GH): Stimulates growth.
  • Prolactin: Stimulates milk production.
  • Follicle-stimulating hormone (FSH): Stimulates gamete production.
  • Luteinizing hormone (LH): Stimulates ovulation in females and testosterone production in males.
  • Thyroid-stimulating hormone (TSH): Stimulates the thyroid gland.
  • Adrenocorticotropic hormone (ACTH): Stimulates the adrenal cortex.

Thyroid Hormone

• Thyroid hormone (T3 and T4): Stimulates metabolism.
• Hyperthyroidism: Excessive thyroid hormone.
• Hypothyroidism: Insufficient thyroid hormone.
• Iodine Deficiency: Can lead to goiter.

Parathyroid Hormone (PTH) and Calcitonin

• PTH: Increases blood calcium levels.
• Calcitonin: Decreases blood calcium levels.

Adrenal Glands

• Adrenal Medulla: Secretes epinephrine and norepinephrine.
  • Epinephrine and Norepinephrine: Increase blood glucose, blood pressure, and respiration.
• Adrenal Cortex: Secretes corticosteroids.
  • Glucocorticoids (e.g., cortisol): Increase blood glucose and suppress the immune system.
  • Mineralocorticoids (e.g., aldosterone): Promote sodium and water reabsorption in the kidneys.

Pancreas

• Insulin: Decreases blood glucose levels.
• Glucagon: Increases blood glucose levels.
• Diabetes Mellitus: Caused by insulin deficiency or resistance.
  • Type 1 Diabetes: Autoimmune destruction of insulin-producing cells.
  • Type 2 Diabetes: Insulin resistance.

Gonads

• Testes (males):
  • Androgens (e.g., testosterone): Promote development of male secondary sex characteristics and sperm production.
• Ovaries (females):
  • Estrogens (e.g., estradiol): Promote development of female secondary sex characteristics and regulate the menstrual cycle.
  • Progesterone: Prepares the uterus for pregnancy.

Pineal Gland

• Melatonin: Regulates sleep cycles.

Evolution of Hormone Function

• Hormones have diverse functions in different animal groups.
• Prolactin has over 300 separate functions in different vertebrate species.

Disruptors

• Foreign molecules that can disrupt hormone signaling pathways.
• Examples: Some pesticides and plastics.

Diagram Description

• The diagram illustrates the human endocrine system along with the locations of major endocrine glands.
• Pineal, Pituitary, Thyroid, and Parathyroid glands are situated in the head and neck.
• Thymus is located in the chest.
• Adrenal glands reside atop kidneys.
• Pancreas sits in the abdomen.
• Ovaries are located in the pelvic region of females and testes in the scrotum of males.

Immune System

• Innate Immunity: A set of defenses that are always active.
• Adaptive Immunity: Develops more slowly and provides long-lasting immunity.

Innate Immunity

• Barrier Defenses:
  • Skin: Provides a physical barrier.
  • Mucous membranes: Trap pathogens.
  • Secretions: Lysozyme in tears and antimicrobial peptides.
• Internal Defenses:
  • Phagocytic cells: Engulf and destroy pathogens.
  • Natural killer cells: Kill infected cells.
  • Antimicrobial proteins: Interferons and complement.
  • Inflammatory response: Redness, swelling, heat, and pain.

Adaptive Immunity

• Lymphocytes: T cells and B cells.
• Antigen: A foreign molecule that elicits an adaptive immune response.
• Antigen receptor: A protein on lymphocytes that binds to an antigen.
• Major Histocompatibility Complex (MHC): Molecules that present antigens to T cells.
• Humoral Immune Response: B cells produce antibodies that neutralize pathogens.
• Cell-Mediated Immune Response: T cells destroy infected cells.

B Cells

• B cell receptor: Binds to specific antigens.
• Plasma cells: Secrete antibodies.
• Antibodies: Mark pathogens for destruction.

T Cells

• Helper T cells: Activate B cells and cytotoxic T cells.
• Cytotoxic T cells: Kill infected cells.

Active vs. Passive Immunity

• Active Immunity: Develops after exposure to an antigen.
• Passive Immunity: Transfer of antibodies from one individual to another.

Immune System Malfunctions

• Allergies: Exaggerated responses to certain antigens.
• Autoimmune diseases: The immune system attacks the body's own cells.
• Immunodeficiency diseases: The immune system is weakened or absent.

HIV

• Human Immunodeficiency Virus (HIV): Infects helper T cells.
• Acquired Immunodeficiency Syndrome (AIDS): Caused by HIV.

Diagram Description

• Illustrates steps and components of the inflammatory response.
• Involves bacteria entering a wound, mast cells releasing histamine, macrophages phagocytizing pathogens, and neutrophils/macrophages killing pathogens.

Cancer and Immunity

• Tumor cells: Can suppress the immune system.
• Immunotherapy: Using the immune system to fight cancer.

Diagram Description

• Humoral and Cell-Mediated responses are seen in an "Adaptive Immunity" diagram.
• Involves B cells, Plasma cell produce antibodies, and the Antibodies binding to antigens to mark pathogens for destruction.

Coronavirus

• SARS-CoV-2: The virus that causes COVID-19.
• Spike protein: Used to enter host cells.
• mRNA vaccines: Teach our cells to make virus particles, which activate immune responses.

Reglas de Inferencia (Rules of Inference)

• Logical forms that allow deriving a conclusion from premises. Premises' truth guarantees the conclusion's truth.

Reglas de Inferencia Proposicionales (Propositional Inference Rules)

• Modus Ponens (MP)
  • Premise: $P \rightarrow Q$
  • Premise: $P$
  • Conclusion: $\therefore Q$
• Modus Tollens (MT)
• Premise: $P \rightarrow Q$
• Premise: $\neg Q$
• Conclusion: $\therefore \neg P$
• Silogismo Hipotético (Hypothetical Syllogism) (HS)
  • Premise: $P \rightarrow Q$
  • Premise: $Q \rightarrow R$
  • Conclusion: $\therefore P \rightarrow R$
• Silogismo Disyuntivo (Disjunctive Syllogism)(DS)
  • Premise: $P \lor Q$
  • Premise: $\neg P$
  • Conclusion: $\therefore Q$
• Adición (Addition) (ADD)
  • Premise: $P$
  • Conclusion: $\therefore P \lor Q$
• Simplificación (Simplification) (SIMP)
  • Premise: $P \land Q$
  • Conclusion: $\therefore P$
• Conjunción (Conjunction) (CONJ)
  • Premise: $P$
  • Premise: $Q$
  • Conclusion: $\therefore P \land Q$
• Dilema Constructivo (Constructive Dilemma) (CD)
  • Premise: $(P \rightarrow Q) \land (R \rightarrow S)$
  • Premise: $P \lor R$
  • Conclusion: $\therefore Q \lor S$

Reglas de Inferencia Cuantificacionales (Quantificational Inference Rules)

• Instanciación Universal (Universal Instantiation) (UI)
  • Premise: $\forall x P(x)$
  • Conclusion: $\therefore P(a)$ (where is an object of the domain)
• Generalización Universal (Universal Generalization)(UG)
  • Premise: $P(a)$ (where is an arbitrary object of the domain)
  • Conclusion: $\therefore \forall x P(x)$
• Instanciación Existencial (Existential Instantiation) (EI)
  • Premise: $\exists x P(x)$
  • Conclusion: $\therefore P(c)$ (where is a new object of the domain)
• Generalización Existencial (Existential Generalization) (EG)
  • Premise: $P(a)$ (where is an object of the domain)
  • Conclusion: $\therefore \exists x P(x)$

Notas (Notes)

• Rules are fundamental in derivations & theorem demonstrations.

Kriging-Based Optimization

Kriging models enhance aerodynamic characteristic approximations, reducing CFD costs via surrogate modeling.

Optimization & Weighting Function

Optimization of design includes low-fidelity and high-fidelity data. Also, data is balanced with the function.

Genetic Algorithm

Objective is to maximize lift-to-drag ratio

Results

Achieves design with maximized lift-to-drag ratio.

Methodology

Parametrization of airfoil geometry shape functions.

Results

The optimized airfoil design achieves a significant improvement in L/D ratio.

Methodology

Optimization couples genetic algorithm to CFD.

Objective

Aim is designing an airfoil that can provide a high lift coefficient.

Results

An optimized airfoil improves over an original version.

Methodology

Uses KSRS.

Objective

Objective to optimize given design restraints.

Results

Enables search and assessment w/limited CFD counts.

Methodology

Uses Kriging and adaptive sampling model

Objective

Design is done through maximizing lift-to-drag by using previous methodology outlined.

Results

Results shows efficient improvement within a limited computation constraint.

Methodology

Uses quasi-Newton method with Bezier functions.

Objective

Objective is to minimize drag but ensure lift and area restrictions.

Results

The proposed method reduces the drag profiles while satisfying both lift and area limits.

Objective

Learn the measure distance to an object using sound and return time

Background

Formula: $$Distance = \frac{Speed of Sound \times Time}{2}$$

Procedure

Connect ultrasonic to board upload code

Data Collection

Analysis

• Error calculations
• Graph of results
• Discuss errors

Conclusion

Learned concepts for experiments and results

Function Logarithm

Natural logarithm is noted as ln.

Definition

It is from $]0; +\infty[$ and is a primitive

Properties

• $\ln(1) = 0$
• $\ln(e) = 1$
• $\ln(x) = \int_1^x \frac{1}{t} dt$
• derivative is defined as $\ln'(x) = \frac{1}{x}$
• strictly increasing

Algebric properties

• $\ln(ab) = \ln(a) + \ln(b)$
• $\ln(\frac{a}{b}) = \ln(a) - \ln(b)$
• $\ln(\frac{1}{b}) = -\ln(b)$
• $\ln(a^n) = n \ln(a)$
• $\ln(\sqrt{a}) = \frac{1}{2} \ln(a)$

Limits

• $\lim_{x \to +\infty} \ln(x) = +\infty$
• $\lim_{x \to 0} \ln(x) = -\infty$
• $\lim_{x \to +\infty} \frac{\ln(x)}{x} = 0$
• $\lim_{x \to 0} x \ln(x) = 0$
• $\lim_{x \to 1} \frac{\ln(x)}{x-1} = 1$
• $\lim_{h \to 0} \frac{\ln(1+h)}{h} = 1$

Derivatives

• let $u$ an deriable and strictly positive so:
• $(\ln(u))' = \frac{u'}{u}$

Table

Overview of Regular Expressions

Regular expressions (regex) define search patterns to find/replace text, validate input, or extract data.

Syntax

Regex syntax includes literals and meta-characters, with particular meaning.

Definition of multiple aspects of the meta-characters and their explanations

Meta-characters and characters have their own purpose and can be viewed in the table in the prompt

Definition of multiple aspects of the character classes and their explanations

Character classes and characters have their own purpose and can be viewed in the table in the prompt

Definition of multiple aspects of the quantifiers and their explanations

quantifiers and characters have their own purpose and can be viewed in the table in the prompt

Examples of regular expressions

Examples of Emails, phone number, dates, etc. have their own purpose and can be viewed in the table in the prompt

Explanation of "re" Library tool in python

The function are also defined there along with a usage

Tips and Tricks

Helps to have understanding over the code such as: Raw String, Testing, Comments, Keep code simple

Advanced Concempts

There are advanced assertions that are complex