Law of Conservation of Matter Lab: Teacher Notes
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Modeling Conservation of Mass
Modeling Conservation of Mass How is mass conserved (protected from loss)? Imagine an evening campfire. As the wood burns, you notice that the logs have become a small pile of ashes. What happened? Was the wood destroyed by the fire? A scientific principle called the law of conservation of mass states that matter is neither created nor destroyed. So, what happened to the wood? Think back. Did you observe smoke rising from the fire? When wood burns, atoms in the wood combine with oxygen atoms in the air in a chemical reaction called combustion. The products of this burning reaction are ashes as well as the carbon dioxide and water vapor in smoke. The gases escape into the air. We also know from the law of conservation of mass that the mass of the reactants must equal the mass of all the products. How does that work with the campfire? mass – a measure of how much matter is present in a substance law of conservation of mass – states that the mass of all reactants must equal the mass of all products and that matter is neither created nor destroyed If you could measure the mass of the wood and oxygen before you started the fire and then measure the mass of the smoke and ashes after it burned, what would you find? The total mass of matter after the fire would be the same as the total mass of matter before the fire. Therefore, matter was neither created nor destroyed in the campfire; it just changed form. The same atoms that made up the materials before the reaction were simply rearranged to form the materials left after the reaction. -
The First Law of Thermodynamics for Closed Systems A) the Energy
Chapter 3: The First Law of Thermodynamics for Closed Systems a) The Energy Equation for Closed Systems We consider the First Law of Thermodynamics applied to stationary closed systems as a conservation of energy principle. Thus energy is transferred between the system and the surroundings in the form of heat and work, resulting in a change of internal energy of the system. Internal energy change can be considered as a measure of molecular activity associated with change of phase or temperature of the system and the energy equation is represented as follows: Heat (Q) Energy transferred across the boundary of a system in the form of heat always results from a difference in temperature between the system and its immediate surroundings. We will not consider the mode of heat transfer, whether by conduction, convection or radiation, thus the quantity of heat transferred during any process will either be specified or evaluated as the unknown of the energy equation. By convention, positive heat is that transferred from the surroundings to the system, resulting in an increase in internal energy of the system Work (W) In this course we consider three modes of work transfer across the boundary of a system, as shown in the following diagram: Source URL: http://www.ohio.edu/mechanical/thermo/Intro/Chapt.1_6/Chapter3a.html Saylor URL: http://www.saylor.org/me103#4.1 Attributed to: Israel Urieli www.saylor.org Page 1 of 7 In this course we are primarily concerned with Boundary Work due to compression or expansion of a system in a piston-cylinder device as shown above. -
Law of Conversation of Energy
Law of Conservation of Mass: "In any kind of physical or chemical process, mass is neither created nor destroyed - the mass before the process equals the mass after the process." - the total mass of the system does not change, the total mass of the products of a chemical reaction is always the same as the total mass of the original materials. "Physics for scientists and engineers," 4th edition, Vol.1, Raymond A. Serway, Saunders College Publishing, 1996. Ex. 1) When wood burns, mass seems to disappear because some of the products of reaction are gases; if the mass of the original wood is added to the mass of the oxygen that combined with it and if the mass of the resulting ash is added to the mass o the gaseous products, the two sums will turn out exactly equal. 2) Iron increases in weight on rusting because it combines with gases from the air, and the increase in weight is exactly equal to the weight of gas consumed. Out of thousands of reactions that have been tested with accurate chemical balances, no deviation from the law has ever been found. Law of Conversation of Energy: The total energy of a closed system is constant. Matter is neither created nor destroyed – total mass of reactants equals total mass of products You can calculate the change of temp by simply understanding that energy and the mass is conserved - it means that we added the two heat quantities together we can calculate the change of temperature by using the law or measure change of temp and show the conservation of energy E1 + E2 = E3 -> E(universe) = E(System) + E(Surroundings) M1 + M2 = M3 Is T1 + T2 = unknown (No, no law of conservation of temperature, so we have to use the concept of conservation of energy) Total amount of thermal energy in beaker of water in absolute terms as opposed to differential terms (reference point is 0 degrees Kelvin) Knowns: M1, M2, T1, T2 (Kelvin) When add the two together, want to know what T3 and M3 are going to be. -
Chapter 6. Time Evolution in Quantum Mechanics
6. Time Evolution in Quantum Mechanics 6.1 Time-dependent Schrodinger¨ equation 6.1.1 Solutions to the Schr¨odinger equation 6.1.2 Unitary Evolution 6.2 Evolution of wave-packets 6.3 Evolution of operators and expectation values 6.3.1 Heisenberg Equation 6.3.2 Ehrenfest’s theorem 6.4 Fermi’s Golden Rule Until now we used quantum mechanics to predict properties of atoms and nuclei. Since we were interested mostly in the equilibrium states of nuclei and in their energies, we only needed to look at a time-independent description of quantum-mechanical systems. To describe dynamical processes, such as radiation decays, scattering and nuclear reactions, we need to study how quantum mechanical systems evolve in time. 6.1 Time-dependent Schro¨dinger equation When we first introduced quantum mechanics, we saw that the fourth postulate of QM states that: The evolution of a closed system is unitary (reversible). The evolution is given by the time-dependent Schrodinger¨ equation ∂ ψ iI | ) = ψ ∂t H| ) where is the Hamiltonian of the system (the energy operator) and I is the reduced Planck constant (I = h/H2π with h the Planck constant, allowing conversion from energy to frequency units). We will focus mainly on the Schr¨odinger equation to describe the evolution of a quantum-mechanical system. The statement that the evolution of a closed quantum system is unitary is however more general. It means that the state of a system at a later time t is given by ψ(t) = U(t) ψ(0) , where U(t) is a unitary operator. -
Key Concepts: Conservation of Mass, Momentum, Energy Fluid: a Material
Key concepts: Conservation of mass, momentum, energy Fluid: a material that deforms continuously and permanently under the application of a shearing stress, no matter how small. Fluids are either gases or liquids. (Under very specialized conditions, a phase of intermediate properties can be stable, but we won’t consider that possibility.) In liquids, the molecules are relatively closely spaced, allowing the magnitude of their (attractive, electrically-based) interaction energy to be of the same magnitude as their kinetic energy. As a result, they exist as a loose collection of clusters. In gases, the molecules are much more widely separated, so the kinetic energy (at a given temperature, identical to that in the liquid) is far greater than the interaction energy (much less than in the liquid), and molecule do not form clusters. In a liquid, the molecules themselves typically occupy a few percent of the total space available; in a gas, they occupy a few thousandths of a percent. Nevertheless, for our purposes, all fluids are considered to be continua (no voids or holes).The absence of significant intermolecular attraction allows gases to fill whatever volume is available to them, whereas the presence of such attraction in liquids prevents them from doing so. The attractive forces in liquid water are unusually strong, compared to other liquids. Properties of Fluids: m Density is mass/volume: ρ = . The density of liquid water is V 3 o −3 3 ~1.0 kg/m ; that of air at 20 C is ~1.2x10 kg/m . mg W Specific weight is weight/volume: γ = = = ρg V V C:\Adata\CLASNOTE\342\Class Notes\Key concepts_Topic 1.doc 1 γ Specific gravity is density normalized to the density of water: sg..= i γ w V 1 Specific volume is volume/mass: V = = m ρ Bulk modulus or modulus of elasticity is the pressure change per dp dp fractional change in volume or density: E =− = . -
1. Define Open, Closed, Or Isolated Systems. If You Use an Open System As a Calorimeter, What Is the State Function You Can Calculate from the Temperature Change
CH301 Worksheet 13b Answer Key—Internal Energy Lecture 1. Define open, closed, or isolated systems. If you use an open system as a calorimeter, what is the state function you can calculate from the temperature change. If you use a closed system as a calorimeter, what is the state function you can calculate from the temperature? Answer: An open system can exchange both matter and energy with the surroundings. Δ H is measured when an open system is used as a calorimeter. A closed system has a fixed amount of matter, but it can exchange energy with the surroundings. Δ U is measured when a closed system is used as a calorimeter because there is no change in volume and thus no expansion work can be done. An isolated system has no contact with its surroundings. The universe is considered an isolated system but on a less profound scale, your thermos for keeping liquids hot approximates an isolated system. 2. Rank, from greatest to least, the types internal energy found in a chemical system: Answer: The energy that holds the nucleus together is much greater than the energy in chemical bonds (covalent, metallic, network, ionic) which is much greater than IMF (Hydrogen bonding, dipole, London) which depending on temperature are approximate in value to motional energy (vibrational, rotational, translational). 3. Internal energy is a state function. Work and heat (w and q) are not. Explain. Answer: A state function (like U, V, T, S, G) depends only on the current state of the system so if the system is changed from one state to another, the change in a state function is independent of the path. -
Chapter 15 - Fluid Mechanics Thursday, March 24Th
Chapter 15 - Fluid Mechanics Thursday, March 24th •Fluids – Static properties • Density and pressure • Hydrostatic equilibrium • Archimedes principle and buoyancy •Fluid Motion • The continuity equation • Bernoulli’s effect •Demonstration, iClicker and example problems Reading: pages 243 to 255 in text book (Chapter 15) Definitions: Density Pressure, ρ , is defined as force per unit area: Mass M ρ = = [Units – kg.m-3] Volume V Definition of mass – 1 kg is the mass of 1 liter (10-3 m3) of pure water. Therefore, density of water given by: Mass 1 kg 3 −3 ρH O = = 3 3 = 10 kg ⋅m 2 Volume 10− m Definitions: Pressure (p ) Pressure, p, is defined as force per unit area: Force F p = = [Units – N.m-2, or Pascal (Pa)] Area A Atmospheric pressure (1 atm.) is equal to 101325 N.m-2. 1 pound per square inch (1 psi) is equal to: 1 psi = 6944 Pa = 0.068 atm 1atm = 14.7 psi Definitions: Pressure (p ) Pressure, p, is defined as force per unit area: Force F p = = [Units – N.m-2, or Pascal (Pa)] Area A Pressure in Fluids Pressure, " p, is defined as force per unit area: # Force F p = = [Units – N.m-2, or Pascal (Pa)] " A8" rea A + $ In the presence of gravity, pressure in a static+ 8" fluid increases with depth. " – This allows an upward pressure force " to balance the downward gravitational force. + " $ – This condition is hydrostatic equilibrium. – Incompressible fluids like liquids have constant density; for them, pressure as a function of depth h is p p gh = 0+ρ p0 = pressure at surface " + Pressure in Fluids Pressure, p, is defined as force per unit area: Force F p = = [Units – N.m-2, or Pascal (Pa)] Area A In the presence of gravity, pressure in a static fluid increases with depth. -
First Law of Thermodynamics Control Mass (Closed System)
First Law of Thermodynamics Reading Problems 3-2 ! 3-7 3-40, 3-54, 3-105 5-1 ! 5-2 5-8, 5-25, 5-29, 5-37, 5-40, 5-42, 5-63, 5-74, 5-84, 5-109 6-1 ! 6-5 6-44, 6-51, 6-60, 6-80, 6-94, 6-124, 6-168, 6-173 Control Mass (Closed System) In this section we will examine the case of a control surface that is closed to mass flow, so that no mass can escape or enter the defined control region. Conservation of Mass Conservation of Mass, which states that mass cannot be created or destroyed, is implicitly satisfied by the definition of a control mass. Conservation of Energy The first law of thermodynamics states “Energy cannot be created or destroyed it can only change forms”. energy entering - energy leaving = change of energy within the system Sign Convention Cengel Approach Heat Transfer: heat transfer to a system is positive and heat transfer from a system is negative. Work Transfer: work done by a system is positive and work done on a system is negative. For instance: moving boundary work is defined as: Z 2 Wb = P dV 1 During a compression process, work is done on the system and the change in volume goes negative, i.e. dV < 0. In this case the boundary work will also be negative. 1 Culham Approach Using my sign convention, the boundary work is defined as: Z 2 Wb = − P dV 1 During a compression process, the change in volume is still negative but because of the negative sign on the right side of the boundary work equation, the bound- ary work directed into the system is considered positive. -
Chapter 9 – Center of Mass and Linear Momentum I
Chapter 9 – Center of mass and linear momentum I. The center of mass - System of particles / - Solid body II. Newton’s Second law for a system of particles III. Linear Momentum - System of particles / - Conservation IV. Collision and impulse - Single collision / - Series of collisions V. Momentum and kinetic energy in collisions VI. Inelastic collisions in 1D -Completely inelastic collision/ Velocity of COM VII. Elastic collisions in 1D VIII. Collisions in 2D IX. Systems with varying mass X. External forces and internal energy changes I. Center of mass The center of mass of a body or a system of bodies is a point that moves as though all the mass were concentrated there and all external forces were applied there. - System of particles: General: m1x1 m2 x2 m1x1 m2 x2 xcom m1 m2 M M = total mass of the system - The center of mass lies somewhere between the two particles. - Choice of the reference origin is arbitrary Shift of the coordinate system but center of mass is still at the same relative distance from each particle. I. Center of mass - System of particles: m2 xcom d m1 m2 Origin of reference system coincides with m1 3D: 1 n 1 n 1 n xcom mi xi ycom mi yi zcom mi zi M i1 M i1 M i1 1 n rcom miri M i1 - Solid bodies: Continuous distribution of matter. Particles = dm (differential mass elements). 3D: 1 1 1 xcom x dm ycom y dm zcom z dm M M M M = mass of the object M Assumption: Uniform objects uniform density dm dV V 1 1 1 Volume density xcom x dV ycom y dV zcom z dV V V V Linear density: λ = M / L dm = λ dx Surface density: σ = M / A dm = σ dA The center of mass of an object with a point, line or plane of symmetry lies on that point, line or plane. -
Discipline in Thermodynamics
energies Perspective Discipline in Thermodynamics Adrian Bejan Department of Mechanical Engineering and Materials Science, Duke University, Durham, NC 27708-0300, USA; [email protected] Received: 24 April 2020; Accepted: 11 May 2020; Published: 15 May 2020 Abstract: Thermodynamics is a discipline, with unambiguous concepts, words, laws and usefulness. Today it is in danger of becoming a Tower of Babel. Its key words are being pasted brazenly on new concepts, to promote them with no respect for their proper meaning. In this brief Perspective, I outline a few steps to correct our difficult situation. Keywords: thermodynamics; discipline; misunderstandings; disorder; entropy; second law; false science; false publishing 1. Our Difficult Situation Thermodynamics used to be brief, simple and unambiguous. Today, thermodynamics is in a difficult situation because of the confusion and gibberish that permeate through scientific publications, popular science, journalism, and public conversations. Thermodynamics, entropy, and similar names are pasted brazenly on new concepts in order to promote them, without respect for their proper meaning. Thermodynamics is a discipline, a body of knowledge with unambiguous concepts, words, rules and promise. Recently, I made attempts to clarify our difficult situation [1–4], so here are the main ideas: The thermodynamics that in the 1850s joined science serves now as a pillar for the broadest tent, which is physics. From Carnot, Rankine, Clausius, and William Thomson (Lord Kelvin) came not one but two laws: the law of energy conservation (the first law) and the law of irreversibility (the second law). The success of the new science has been truly monumental, from steam engines and power plants of all kinds, to electric power in every outlet, refrigeration, air conditioning, transportation, and fast communication today. -
Chemical Engineering Thermodynamics
CHEMICAL ENGINEERING THERMODYNAMICS Andrew S. Rosen SYMBOL DICTIONARY | 1 TABLE OF CONTENTS Symbol Dictionary ........................................................................................................................ 3 1. Measured Thermodynamic Properties and Other Basic Concepts .................................. 5 1.1 Preliminary Concepts – The Language of Thermodynamics ........................................................ 5 1.2 Measured Thermodynamic Properties .......................................................................................... 5 1.2.1 Volume .................................................................................................................................................... 5 1.2.2 Temperature ............................................................................................................................................. 5 1.2.3 Pressure .................................................................................................................................................... 6 1.3 Equilibrium ................................................................................................................................... 7 1.3.1 Fundamental Definitions .......................................................................................................................... 7 1.3.2 Independent and Dependent Thermodynamic Properties ........................................................................ 7 1.3.3 Phases ..................................................................................................................................................... -
Chapter 5 the Laws of Thermodynamics: Entropy, Free
Chapter 5 The laws of thermodynamics: entropy, free energy, information and complexity M.W. Collins1, J.A. Stasiek2 & J. Mikielewicz3 1School of Engineering and Design, Brunel University, Uxbridge, Middlesex, UK. 2Faculty of Mechanical Engineering, Gdansk University of Technology, Narutowicza, Gdansk, Poland. 3The Szewalski Institute of Fluid–Flow Machinery, Polish Academy of Sciences, Fiszera, Gdansk, Poland. Abstract The laws of thermodynamics have a universality of relevance; they encompass widely diverse fields of study that include biology. Moreover the concept of information-based entropy connects energy with complexity. The latter is of considerable current interest in science in general. In the companion chapter in Volume 1 of this series the laws of thermodynamics are introduced, and applied to parallel considerations of energy in engineering and biology. Here the second law and entropy are addressed more fully, focusing on the above issues. The thermodynamic property free energy/exergy is fully explained in the context of examples in science, engineering and biology. Free energy, expressing the amount of energy which is usefully available to an organism, is seen to be a key concept in biology. It appears throughout the chapter. A careful study is also made of the information-oriented ‘Shannon entropy’ concept. It is seen that Shannon information may be more correctly interpreted as ‘complexity’rather than ‘entropy’. We find that Darwinian evolution is now being viewed as part of a general thermodynamics-based cosmic process. The history of the universe since the Big Bang, the evolution of the biosphere in general and of biological species in particular are all subject to the operation of the second law of thermodynamics.