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Solved: Liquid helium is stored at its boiling-point

Physics, | 9th Edition | ISBN: 9780470879528 | Authors: John D. Cutnell, Kenneth W. Johnson ISBN: 9780470879528 211

Solution for problem 13.66 Chapter 13

Physics, | 9th Edition

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Physics, | 9th Edition | ISBN: 9780470879528 | Authors: John D. Cutnell, Kenneth W. Johnson

Physics, | 9th Edition

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Problem 13.66

Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical container (r 0.30 m). The container is a perfect blackbody radiator. The container is surrounded by a spherical shield whose temperature is 77 K. A vacuum exists in the space between the container and the shield. The latent heat of vaporization for helium is 2.1 104 J/kg. What mass of liquid helium boils away through a venting valve in one hour?

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PHYS 1010 Midterm Study Guide Scientific Method ­ Hypothesis is used to predict the results of an experiment ­ Repeated experiments verify or nullify the hypothesis ­ "Code of ethics": scientists publish their results for review by other scientists ­ It is impossible to completely prove a theory ­ Repeatedly verified theories are called laws ­ Bottom­up method: science starts with evidence and facts and builds on those to create eventual theories Vectors and Coordinate Systems (Motion) ­ Mechanics: deals with motion and the forces that cause motion ­ Galileo developed the way we think about physical motion: the relationships between time, position, velocity, and acceleration ­ Position and time ­ We measure position by creating an arbitrary coordinate system/reference point around an object and describing the position as an (x, y) coordinate ­ Vector: describes both magnitude and direction ­ We add vectors "tip to tail" ­ Breaking vectors into their x and y components simplifies adding ­ Two vectors are equal if they have the same magnitude and direction, regardless of the starting points of the vectors ­ Scalar: describes a magnitude of physical quantity (not a direction) ­ Velocity: how fast an object is moving (speed and direction) ­ Instantaneous velocity: velocity at a certain point in time ­ Average velocity ­ Acceleration: change in velocity with time ­ Occurs with a change in magnitude or direction of the velocity vector ­ Every object is accelerated by gravity at the same constant rate ­ Throwing an object up in the air results in gravity decelerating the object until it reaches zero velocity, and then moving it back downward ­ Projectile motion: moving up/down AND left/right ­ Vertical acceleration doesn't affect horizontal velocity Forces ­ Force: a push or pull that causes an object to accelerate ­ Require an agent: something that acts to move the object ­ Linear superposition of forces: multiple forces operating on an object, add forces together to solve for net force ­ Application of force causes motion ­ Inertia: the ability of an object to resist acceleration ­ Newton's First Law: bodies at rest stay at rest, and bodies in motion stay in motion (unless acted upon by a force) ­ No force = no change in velocity ­ Newton's Second Law: force = (mass)(acceleration) ­ Newton's Third Law: for every action, there is an equal and opposite reaction ­ When two bodies interact, the force on the bodies from each other are always equal and opposite ­ Weight: the measure of the force of gravity on a mass ­ Apparent weight: a sensation evident when we are in an accelerating reference frame (ex. we feel heavier in ascending elevators) ­ Gravitational force ­ Weight is a magnitude of gravitational force ­ Newton's Law of Gravity: the force of gravity between two objects depends on the mass of the two objects and the distance between them 2 ­ Gravity near the earth's surface is constant (9.8 m/s ) because the distance between us, and the center of the earth, stays relatively constant ­ Normal force: forces that balance gravitational force so that objects aren't constantly moving ­ Always perpendicular to the surface ­ Frictional force: force that opposes attempted motion ­ Caused by the connecting and breaking of contact points when objects slide against one another ­ Static friction occurs when two objects are not moving relative to each other, and opposes the initial motion ­ Kinetic friction occurs when two objects are in motion relative to each other, and opposes the continuing motion ­ Coefficient of friction: relates the normal force and frictional force ­ Drag force: an opposing force that depends on the velocity of an object ­ Occurs when an object moves through a fluid (gas or liquid) ­ When drag force equals gravity, acceleration reaches zero and the object falls at a constant velocity (terminal velocity) ­ Larger cross­sectional area of object results in a higher drag force ­ Tensional force: indirect force transmitted to an object by a string or rope attached to the object ­ Pulling on the rope distributes force along the length of the rope and then accelerates the object ­ Thrust force: occurs when an object propels itself without necessarily contacting anything externally ­ When an object expels particles away from itself, the object experiences an equal and opposite reaction (Newton's 3rd Law of Motion) ­ Electromagnetic forces: action­at­a­distance forces that arise from the presence and motion of electrons ­ Nuclear forces: hold nuclei together and sub­sub­atomic particles together ­ Torque: a linear force that causes and object to rotate ­ Only created if the force is perpendicular to the position vector ­ Uniform circular motion: when the speed of an object moving in a circular path is constant ­ Velocity is changing because direction is changing (so it is accelerating) ­ Centripetal acceleration: causes curved path ­ "Centrifugal" forces ­ Not real according to Newton's laws ­ As long as there is a normal force pushing on an object, it will not fall ­ Rollercoaster example: nothing is holding cart on the loop, but the track is curving steeper than the cart would fall by itself ­ Circular orbits: gravity working solely as a centripetal force Momentum ­ Conservation laws: things aren't created or destroyed, but conserved ­ Momentum involves mass (inertia) and velocity ­ Force: change in momentum over some time span ­ Linear momentum is conserved (no force = no change in momentum) ­ Angular momentum: spinning momentum ­ Conservation of angular momentum: angular momentum is the same throughout any period of time ­ Decreased radius/size ­­> faster spin ­ Systems of particles ­ Objects are made up of particles that don't always move in the same way ­ We discuss systems of particles in terms of their center of mass (COM) ­ COM: point that moves as though all of the mass were concentrated there and all forces were applied there ­ The COM will follow the path as predicted for a single particle ­ Allows us to discuss real­life systems without describing every particle in the object individually ­ Impulse force: force that is exerted after elastic bonds between particles contract upon collision ­ Longer collision ­­> smaller force Energy and Work ­ Energy: a scalar quantity associated with the condition of one or more objects ­ Kinetic energy: energy from the motion of an object ­ Work: energy transferred to or from an object by means of force acting on an object ­ Changing energy = work = (force)(displacement) ­ A force is necessary to change motion ­ Positive work: energy transferred to an object ­ Negative work: energy transferred from an object ­ Potential energy: the energy an object has due to position ­ "Stored" inside an object ­ Change in kinetic energy ­ Conservative and non­conservative forces ­ Upward and downward forces of an object thrown upward have the same speed and kinetic energy. Therefore, the kinetic energy is "conserved" when dealing with gravitational force ­ A "conservative" force will return the work it does on an object when the object is turned to its original position ­ Gravitational force is conservative and frictional force is non­ conservative ­ Conservation of mechanical energy ­ Mechanical energy = kinetic energy + potential energy ­ Kinetic energy and potential energy trade­off but total mechanical energy stays the same ­ Thermal energy: motion causes heat ­ Heat: change in temperature that occurs when thermal energy is transferred between to touching objects ­ Positive when energy is transferred to an object from the environment ­ Negative when object loses thermal energy to the environment ­ Always transferred from the hotter object to the colder object ­ Heat transfer ­ Radiation: heat from light ­ Conduction: heat transferred because a hot object touches a cold object ­ Convection: heat transfer by motion of fluid: heated fluid moves away from the object, carrying heat with it ­ Absorption of heat ­ Heat capacity: the amount of energy required to heat up an object ­ Specific heat: heat capacity per unit mass of a substance ­ Metal conducts heat very well; insulating materials like fiberglass and Styrofoam trap air and hold it in place to keep things cool ­ Air almost doesn't conduct heat ­ Thermal expansion: adding kinetic energy to a solid lattice causes atomic bonds to stretch and leads to an expanding of the entire lattice ­ The way we measure temperature ­ Overstretching ­­> change in state of matter ­ Temperature: used to describe a measure of heat ­ Lowest possible limit is 0K when atoms stop vibrating ­ Matter cannot exist below 0K ­ Work done on a system by an external force ­ External forces can do work on a closed system by transferring energy to or from a system ­ Work done against friction becomes thermal energy (heat) ­ Work done against the force of friction is the loss of mechanical energy to thermal energy ­ Conservation of energy: the total amount of energy in a closed system can never change ­ Earth is not a closed system, but universe is ­ Laws of Thermodynamics ­ 0th Law: if objects A and B are each in thermal equilibrium with a third object C, then objects A and B are in thermal equilibrium with each other ­ If something is in one part of a system, then it is in all parts of the system ­ 1st Law: the difference between the transferred thermal energy and change in mechanical energy determines the change in the internal energy of the system ­ 2nd Law: the entropy of a closed system can never decrease ­ 3rd Law: in order to cool something to 0K, you need something colder than 0K, which can't exist as matter. Therefore nothing can be cooled to 0K ­ Entropy: randomness/disorder ­ Many natural processes are irreversible (not symmetric) ­ Problematic because conservation of energy is symmetric and doesn't suggest any kind of direction ­ If an irreversible process occurs in a closed system, the amount of entropy always increases (it can never decrease) ­ Change in entropy is thought to be a factor in our concept of the "arrow of time" ­ Time moving backwards would violate the concept of entropy ­ Heat engines and refrigeration ­ When a hot object and cold object are touching, energy moves from the hot object t the cold object, and we can siphon off that energy as it moves and use it to drive an engine ­ Efficiency is never 100% because some heat must flow to the cold object; however, the energy being transferred to the cold object doesn't do us any good ­ Refrigerators go from hot to cold­ fridges are just reversing the previous flow of energy. We need a heat engine as well as the cooling system Electric Charge ­ Particles have either a positive or negative charge ­ Negatively charged: object contains more negative particles than positive particles ­ Positively charged: object contains more positive particles than negative particles ­ Electrically neutral: object contains equal amounts of positive and negative particles ­ Nature prefers neutral charges ­ The terms "positive" and "negative" don't mean anything; they just refer to the fact that the charges are opposite ­ Electrostatic/electric force: the force that charged particles exert on each other ­ Objects with the same electrical charge repel each other, while objects with opposite electrical charges attract each other ­ Strong electrical charges can induce an opposite charge in a neutrally charged system ­ Grounding can neutralize a system’s charge ­ Grounding: touching an object to the ground (the earth is so big that it can absorb any extra charge without problem) ­ Current: rate at which charge moves past a given point in a given amount of time ­ Charge is quantized (comes in basic units based on electrons that cannot be divided) ­ Charge is conserved (cannot be created or destroyed, only moved around) ­ Charge moving through materials ­ Conductors allow electrons to move freely (ex. metal) ­ Everything can be a conductor with enough electricity ­ Resistance inhibits flow ­ Ohm's law: as potential increases, current increases, and when resistance increases, current decreases (v = IR) I is current, R is resistance, V is voltage ­ Insulators don't allow electrons to move as freely ­ Semi­conductors are somewhere in between ­ Superconductors allow charge to move without hindrance ­ Coulomb’s law: force exerted by charged particles on each other depends on the size of the charge of the particles as well as their distance from one another * Increasing force means opposite charges (attracting particles) ­ Electric fields: electrostatic forces existing around a charged particle ­ We draw electric field using field lines ­ Field lines closer together shows stronger force (flux) ­ Field lines extend away from positive charges and toward negative charges ­ Charged particles have potential energy ­ Electric potential (voltage): potential energy per electrical charge ­ Electric current: flow of electrons in motion (negative to positive) ­ Inserting battery into loop of conductive material creates a flow ­ Series Circuits ­ Battery/power supply: creates a difference in potential energy ­ Path from one end of battery to another (wire or other conductive material) ­­> Electric current ­ Electrons pushed through a resistor, which slows the current down/steals kinetic energy from the electrons to power a machine ­ Power multiple machines by adding multiple resistors to circuit around the circuit ­ Each resistor increases the overall resistance of circuit ­ Parallel circuits ­ Put resistors into a circuit next to each other, creating multiple paths for the electron to move through ­ If one of the paths slows down (because electrons have to slow to enter the resistor), the backed­up electrons move through the next parallel resistor ­ Adding resistors decreases the resistance of the circuit, increasing current flow (like adding lanes to a highway) ­ Too fast of a current is an issue because wires can only hold so much electricity ­ Direct current (DC): current that flows in only one direction ­ Usually used in electronics/devices ­ Alternating current (AC): current alternates direction (60 times/s (60 Hz)), which changes faster than what we can see (20 Hz) ­ Easier to generate and travel over long distances ­ Argument between Tesla (AC) vs. Edison (DC) because AC is dangerous ­ Edison created the electric chair, which used AC ­ Transformers are used to change between AC and DC Magnetism ­ Magnetic fields ­ Magnetic particles are dipoles, and the two poles of a magnet are the North and South poles ­ All magnetic field lines originate from the North Pole and move toward the South Pole ­ We draw magnetic field lines by placing a compass near the magnet and tracing the direction in which the arrow of the compass points (towards the south magnetic pole) ­ Right now the south magnetic pole is at the North Pole of the Earth ­ Earth's poles have switched historically ­ Earth's magnetic poles are not exactly located at the north and South Pole ­ Field lines pass through the magnet and form closed loops ­ Opposite magnetic poles attract each other, and like magnetic poles repel each other ­ Northern lights: magnetic fields crashing down in one place ­ Spin: some particles, like electrons, produce a magnetic field characteristically ­ Permanent magnet: magnetic fields of many particles arranged in a specific manner ­ Some materials let particles float and when they go close to a magnet, the particles will arrange in a way that creates a magnet out of that material ­ Magnetic force only affects moving particles ­ The equation for a magnetic field ­ Tells us which direction the force will accelerate the charged particle (perpendicular to both the direction of the velocity and the magnetic field) ­ Shows that magnetic fields tend to make particles move in a circle ­ Magnetic fields can never increase the kinetic energy of a moving particle, only change the direction ­ Magnetic fields cannot do work * Magnetic fields only exert force on moving charged particles (moving charge is the same as an electric current) ­ Magnetic force on a current­carrying wire ­ Running a current through a wire and putting it in a magnetic field will make the wire move back and forth ­ Electrical current produces a magnetic field ­ Loop of current inside a magnetic field is an electric motor: converts electrical current into mechanical energy ­ Works by alternating the magnetic field/current direction ­ Solenoid: wire wrapped in a cylindrical shape to amplify the magnetic field ­ Solenoids start car engines (magnetic field exerts a force that pushes a button that starts the car) ­ Toroid: a solenoid with ends connected to form a donut ­ Create an amplified magnetic field that force charged particles to move in a circular path ­ Used as particle accelerators ­ Magnetism: moving electricity/charge ­ Magnetism creating electricity ­ "Induction": inducing an electric field ­ Magnet being moved into a loop of wire creates electric current because from the magnet's perspective, those particles are now moving ­ Electricity causing electricity ­ Putting a loop of current next to another loop of current creates induction ­­> Wireless communication ­ Lenz's law ­ Current of a wire inserted into a magnetic loop will induce magnetism that is the opposite direction of the original magnet, so it will "push back" at the magnet being inserted ­ Verifies that there are forces being created, and forces can do work ­ Dropping a magnet through a copper pipe ­ Copper conducts electricity ­ Changing magnetic fields create electricity ­ Current/magnetic field in pipe pushes against magnet (Lenz's law), so the magnet slows down as it falls through pipe ­ Electromagnetism ­ Electricity and magnetism are basically the same thing, they just work in opposite directions ­ Induction and energy transfers ­ Rail guns: conducting wire frame creates magnetic field that pushes one side of moving wire out and gets bigger and bigger; used to fire projectiles ­ Eddy Currents: "whirlpool" currents produced when a solid object moves through a magnetic field ­ Result in lost energy ­ Useful for train brakes ­ Eddy currents created by superconductors create gigantic electric currents with no resistance ­­> huge magnetic field ­­> maglev trains ­ Superconductors only conduct at low temperatures, which is an issue because it's lower than the temperature of liquid nitrogen (used to cool it off); superconductors are difficult to keep cold all the time, which is why we don't use them for everything Maxwell's equations ­ All of these equations together explain everything about electricity and magnetism 1. Definition of electric field 2. Definition of magnetic field 3. Faraday's law: a changing magnetic field creates an electric field 4. Ampere­Maxwell Law: a changing electric field creates a magnetic field ­ Explanation that electromagnetic radiation means that light is made up of waves ­ But waves must travel through a substance­ so how does light travel through space ­ According to Maxwell, light is electricity and magnetism (a wave that doesn't need to travel through anything) ­ Electromagnetic waves ­ Maxwell's equations 3 and 4 explain that light can move through an empty space because it is creating/driving itself with electricity and magnetism ­ Pushing electric charges up and down creates electric waves/electric field which creates a magnetic field, and on and on ­ We can send signals (radio, etc.) that keep moving forever ­ The speed of light is a constant (never changing) ­ Throwing a baseball 20mph means the speed it 20mph ­ Throwing a baseball 20mph out a car while driving 20mph means the speed is 20mph ­ Turning a flashlight on means the speed is constant, but turning a flashlight on while running also results in a constant speed ­ Concept of mass/time/length units is called into question, changes everything we know about physics

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Chapter 13, Problem 13.66 is Solved
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Textbook: Physics,
Edition: 9
Author: John D. Cutnell, Kenneth W. Johnson
ISBN: 9780470879528

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Solved: Liquid helium is stored at its boiling-point