Physics of Technology PHYS 1800

Physics of TechnologyPHYS 1800 Lecture 27 Review for Test 3

PHYSICS OF TECHNOLOGYSpring 2009 Assignment Sheet *Homework Handout

Notes on Test • Covers Chapters 9-11 • ~8 short answer problems or questions (5 point each) • 3 Numerical problems based heavily on the material from the homework and Lab/Demo sessions (20 points each). One problem each from Chapters 9, 10 and 11. • You will have a formula sheet just like the one in the handout. • Test is Thursday March 26 1:30-2:45 in ESLC 46.

Physics of TechnologyPHYS 1800 Lecture 27 Review for Test 3 Introduction and Review

What Do We Need To Measure? • What is the minimum about things we need to know? • Where things are—a length, L • When things are there—a time, t • How thing interact with gravity—a mass, M • How things interact with E&M—a charge, Q • How thing inter act with weak nuclear force • How things interact with strong nuclear force • Random collections of objects—a temperature, T

Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT-1 or m/s) Acceleration—how fast velocity is changing with time (LT-2 or m/s2) Force— what is required to change to motion of a body (MLT-2 or kg-m/s2 or N) Inertia (mass)— a measure of the force needed to change the motion of a body (M) Energy—the potential for an object to do work.(ML2T-2 or kg m2/s2 or N-m or J) Work is equal to the force applied times the distance moved. W = F d Kinetic Energy is the energy associated with an object’s motion. KE=½ mv2 Potential Energy is the energy associated with an objects position. Gravitational potential energy PEgravity=mgh Spring potential energy PEapring= -kx Momentum— the potential of an object to induce motion in another object (MLT-1 or kg-m/s) Angular Momentum and Rotational Energy— the equivalent constants of motion for rotation (MT-1 or kg/s) and (MLT-2 or kg m/s2 or N)

Newton’s Laws in Review • 1st Law—a special case of the 2nd Law for statics, with a=0 or Fnet=0 • An objects velocity remains unchanged, unless a force acts on the object. • 2nd Law(and 1st Law)—How motion of a object is effected by a force. • The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force. • 3rd Law—Forces come from interactions with other objects. • For every action(force),there is an equal but opposite reaction(force).

Energy  Time  Conservation of Energy Energy: The potential to do work. Conservation of Energy: The total energy of a closed system remains constant. • Energy can be converted from one form to another. • Not all forms of energy can be fully recovered.

Momentum and Impulse • Multiply both sides of Newton’s second law by the time interval over which the force acts: • The left side of the equation is impulse, the (average) force acting on an object multiplied by the time interval over which the force acts. • How a force changes the motion of an object depends on both the size of the force and how long the force acts. • The right side of the equation is the change in the momentum of the object. • The momentum of the object is the mass of the object times its velocity.

Impulse-Momentum Principle The impulse acting on an object produces a change in momentum of the object that is equal in both magnitude and direction to the impulse. In analogy, work = change in energy = ΔE

Formulas We Know and Love Formulas as They Will Appear on the Test Sheet

Test 3 Review Concepts Concepts and Terms to Be Familiar With Know what pressure and density are and how this relates to fluids. Know Pascal’s Principle and how to apply it to hydraulics problems. Know how buoyant force is related to pressure and Archimedes’ Principle. Know what an ideal gas is and what the ideal gas law says about pressure volume and temperature of an ideal gas. Understand how conservation of mass is related to flow rate. Understand the difference between laminar and turbulent flow. Understand Bernoulli’s Principle as a fluid form of the conservation of energy. Be able to state the four laws of thermodynamics. Be able to define heat and temperature and explain how they are different. Understand heat capacity, heat of fusion (melting), and heat of vaporization (boiling). Be able to do simple calorimitry problems. Be able to qualitatively explain the difference between the three forms of heat transfer: conduction, convection and radiation. Be able to explain what a heat engine is and what the components of work, high temperature reservoir and low temperature reservoir. What is efficiency of a heat engine? Of a Carnot engine?

Formulas We Know and Love New Formulas as They Will Appear on the Test Sheet

Physics of TechnologyPHYS 1800 Lecture 27 Review for Test 3 Fluids and Pressure

Test 3 Review Concepts Fluids and Pressure Concepts and Terms to Be Familiar With Know what pressure and density are and how this relates to fluids. Know Pascal’s Principle and how to apply it to hydraulics problems. Know how buoyant force is related to pressure and Archimedes’ Principle. Know what an ideal gas is and what the ideal gas law says about pressure volume and temperature of an ideal gas. Understand how conservation of mass is related to flow rate. Understand the difference between laminar and turbulent flow. Understand Bernoulli’s Principle as a fluid form of the conservation of energy.

States of Matter

Pressure • The man weighs more, so he exerts a larger force on the ground. • The woman weighs less, but the force she exerts on the ground is spread over a much smaller area. • Pressure takes into account both force and the area over which the force is applied. • Pressure is the ratio of the force to the area over which it is applied: • Units: 1 N/m2 = 1 Pa (pascal) • Pressure is the quantity that determines whether the soil will yield.

Dennison’s Laws of Fluids • When push comes to shove, fluids are just like other stuff. • Pascal’s Principle: Pressure extends uniformly in all directions in a fluid. • Boyle’s Law: Work on a fluid equals PΔV • Bernoulli’s Principle: Conservation of energy for fluids

Pascal’s Principle • Fluid pushes outward uniformly in all directions when compressed. • Any increase in pressure is transmitted uniformly throughout the fluid. • Pressure exerted on a piston extends uniformly throughout the fluid, causing it to push outward with equal force per unit area on the walls and the bottom of the cylinder. • This is the basis of Pascal’s Principle: • Any change in the pressure of a fluid is transmitted uniformly in all directions throughout the fluid.

Pascal’s Principle for Gases • Gas molecules lack strong interactions. • Pressure is understood as resulting from momentum transfer to the container walls through unbalanced collisions • Pressing on one surface adds force and hence imparts impulse to the gas • That impulse is taken up as added collisons (pressure) on other surfaces • The random nature of the motion of gas particles assures that the force is distributed evenly to all surfaces • For fixed walls, a decrease in V results in an increase in P • For expandable walls (like a balloon) the volume “appears elsewhere to make up for the lost volume

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Pascal’s Principle for Liquids • Liquid molecules have strong interactions. • Liquids do not compress much • Pressure is understood as resulting from momentum transfer to the container walls through unbalanced spring forces • Pressing on one surface adds force that is transferred to other springs • The network nature of the forces on the particles assures that the force is distributed evenly to all surfaces • For expandable walls (like a balloon) the volume “appears elsewhere to make up for the lost volume • For fixed walls, a small decrease in V (a compression) results in a large increase in P • For solids, you can think of the strong forces holding the atoms in there equilibrium positions, equivalent to fixed walls

Archimedes’ Principle • The average density of an object compared to a fluid determines whether the object will sink or float in that liquid. • The upward force that pushes objects back toward the surface in liquids is called the buoyant force. • Archimedes’ Principle: The buoyant force acting on an object fully or partially submerged in a fluid is equal to the weight of the fluid displaced by the object.

Archimedes’ Principle • For example, consider a block submerged in water, suspended from a string. • The pressure of the water pushes on the block from all sides. • Because the pressure increases with depth, the pressure at the bottom of the block is greater than at the top. • There is a larger force (F = PA) pushing up at the bottom than there is pushing down at the top. • The difference between these two forces is the buoyant force. The buoyant force is proportional to both the height and the cross-sectional area of the block, and thus to its volume. The volume of the fluid displaced is directly related to the weight of the fluid displaced.

Flow Rate • The volume of a portion of water of length L flowing past some point in a pipe is the product of the length times the cross-sectional area A, or LA. • The rate at which water moves through the pipe is this volume divided by time: LA / t. • Since L / t = v, the rate of flow = vA.

Laminar vs Turbulent Flow • Laminar flow is smooth flow, with no eddies or other disturbances. • The streamlines are roughly parallel. • The speeds of different layers may vary, but one layer moves smoothly past another. • Turbulent flow does have eddies and whorls; the streamlines are no longer parallel.

Bernoulli’s Principle • How does a large passenger jet manage to get off the ground? • What forces keep it in the air? • How is a ball suspended in mid-air by a leaf blower? • What happens if we do work on a fluid? • Bernoulli’s principle applies conservation of energy to the flow of fluids: • The sum of the pressure plus the • kinetic energy per unit volume of • a flowing fluid must remain constant.

How does pressure vary in pipes and hoses? Pressure Changes with Area • Will the pressure be greatest in the narrow section or the wide section? • The speed will be greater in the narrow section. • To keep the sumP + 1/2 dv2 constant, the pressure must be larger where the fluid speed is smaller (h is fixed). • If the speed increases, the pressure decreases. (This goes against our intuition.) • This can be shown using vertical open pipes as pressure gauges. • The height of the column of water is proportional to the pressure.

Physics of TechnologyPHYS 1800 Lecture 27 Review for Test 3 Temperature and Heat

Test 3 Review Concepts Temperature and Heat Concepts and Terms to Be Familiar With Be able to state the four laws of thermodynamics. Be able to define heat and temperature and explain how they are different. Understand heat capacity, heat of fusion (melting), and heat of vaporization (boiling). Be able to do simple calorimitry problems. Be able to qualitatively explain the difference between the three forms of heat transfer: conduction, convection and radiation.

Dennison’s Laws Thermal Poker(or How to Get a Hot Hand in Physics) • 0th Law: Full House beats Two Pairs • 1st Law: We’re playing the same game (but with a wild card) • 2nd Law: You can’t win in Vegas. • 3rd Law: In fact, you always loose. • 0th Law: Defines Temperature • 1st Law: Conservation of Energy (with heat) • 2nd Law: You can’t recover all heat losses (or defining entropy) • 3rd Law: You can never get to absolute 0.

Heat • What is heat? • What is the relationship between quantity of heat and temperature? • What happens to a body (solid, liquid, gas) when thermal energy is added or removed? Thermal Energy solid Solid: Atoms vibrating in all directions about their fixed equilibrium (lattice) positions. Atoms constantly colliding with each other. Liquid: Atoms still oscillating and colliding with each other but they are free to move so that the long range order (shape) of body is lost. Gas: No equilibrium position, no oscillations, atoms are free and move in perpetual high-speed “zig-zag” dance punctuated by collisions. liquid gas

Temperature and Heat • When two objects at different temperatures are placed in contact, heat will flow from the object with the higher temperature to the object with the lower temperature. • Heat added increases temperature, and heat removed decreases temperature. • Heat and temperature are not the same. • Temperature is a quantity that tells us which direction the heat will flow. Heatis a form of energy. (Here comes conservation of energy!!!)

Gas Behavior and The First Law Consider a gas in a cylinder with a movable piston. If the piston is pushed inward by an external force, work is done on the gas, adding energy to the system. • The force exerted on the piston by the gas equals the pressure of the gas times the area of the piston: • F = PA • The work done equals the force exerted by the piston times the distance the piston moves: • W = Fd = (PA)d = PV

Ideal Gas Behavior • In an isothermal process, the temperature does not change. • The internal energy must be constant. • The change in internal energy, U, is zero. • If an amount of heat Q is added to the gas, an equal amount of work W will be done by the gas on its surroundings, from U = Q - W. • In an isobaric process, the pressure of the gas remains constant. • The internal energy increases as the gas is heated, and so does the temperature. • The gas also expands, removing some of the internal energy. • Experiments determined that the pressure, volume, and absolute temperature of an ideal gas are related by the equation of state: PV = NkTwhere N is the number of molecules and k is Boltzmann’s constant.

Heat and Specific Heat Capacity • The specific heat capacity of a material is the quantity of heat needed to change a unit mass of the material by a unit amount in temperature. • For example, to change 1 gram by 1 Celsius degree. • It is a property of the material, determined by experiment. • The specific heat capacity of water is 1 cal/gC: it takes 1 calorie of heat to raise the temperature of 1 gram of water by 1C. • We can then calculate how much heat must be absorbed by a material to change its temperature by a given amount: Q = mcT where Q = quantity of heat m = mass c = specific heat capacity T = change in temperature

If the specific heat capacity of ice is 0.5 cal/gC°, how much heat would have to be added to 200 g of ice, initially at a temperature of -10°C, to raise the ice to the melting point? • 1,000 cal • 2,000 cal • 4,000 cal • 0 cal m = 200 g c = 0.5 cal/gC° T = -10°C Q = mcT = (200 g)(0.5 cal/gC°)(10°C) = 1,000 cal (heat required to raise the temperature)

+ + + + + + + + + Phase Changes and Latent Heat • When an object goes through a change of phase or state, heat is added or removed without changing the temperature. Instead, the state of matter changes: solid to liquid, for example. • The amount of heat needed per unit mass to produce a phase change is called the latent heat. • The latent heat of fusion of water corresponds to the amount of heat needed to melt one gram of ice. • The latent heat of vaporization of water corresponds to the amount of heat needed to turn one gram of water into steam. Solid

If the specific heat capacity of ice is 0.5 cal/gC°, how much heat would have to be added to 200 g of ice, initially at a temperature of -10°C, to completely melt the ice? • 1,000 cal • 14,000 cal • 16,000 cal • 17,000 cal Lf = 80 cal/g Q = mLf = (200 g)(80 cal/g) = 16,000 cal (heat required to melt the ice) Total heat required to raise the ice to 0 °C and then to melt the ice is: 1,000 cal + 16,000 cal =17,000 cal= 17 kcal

A hot plate is used to transfer 400 cal of heat to a beaker containing ice and water; 500 J of work are also done on the contents of the beaker by stirring. What is the increase in internal energy of the ice-water mixture? W = -500 J Q = 400 cal = (400 cal)(4.19 J/cal) = 1680 J U = Q - W = 1680 J - (-500 J) = 2180 J • 900 J • 1180 J • 1680 J • 2180 J

A hot plate is used to transfer 400 cal of heat to a beaker containing ice and water; 500 J of work are also done on the contents of the beaker by stirring. How much ice melts in this process? Lf= 80 cal/g = (80 cal/g)(4.19 J/cal) = 335 J/g U = mLf m = U/ Lf = (2180 J) / (335 J/g) = 6.5 g • 0.037 g • 0.154 g • 6.5 g • 27.25 g

The Flow of Heat • There are three basic processes for heat flow: • Conduction • Convection • Radiation

The Flow of Heat • In conduction, heat flows through a material when objects at different temperatures are placed in contact with one another.

The Flow of Heat • In convection, heat is transferred by the motion of a fluid containing thermal energy. • Convection is the main method of heating a house. • It is also the main method heat is lost from buildings.

The Flow of Heat • In radiation, heat energy is transferred by electromagnetic waves. • The electromagnetic waves involved in the transfer of heat lie primarily in the infrared portion of the spectrum. • Unlike conduction and convection, which both require a medium to travel through, radiation can take place across a vacuum. • For example, the evacuated space in a thermos bottle. • The radiation is reduced to a minimum by silvering the facing walls of the evacuated space.

Physics of TechnologyPHYS 1800 Lecture 27 Review for Test 3 Heat Engines and the Second Law

Test 3 Review Concepts Heat Engines and the Second Law Concepts and Terms to Be Familiar With Be able to explain what a heat engine is and what the components of work, high temperature reservoir and low temperature reservoir. What is efficiency of a heat engine? Of a Carnot engine?

Heat Engines It is a device that uses input heat to generate useful work. From the 1st Law (Conservation of Energy) In cyclic engines we return to the original state every cycle so What is a heat engine?

Heat Engines All heat engines share these main features of operation: • Thermal energy (heat) is introduced into the engine. • Some of this energy is converted to mechanical work. • Some heat (waste heat) is released into the environment at a temperature lower than the input temperature. What is a heat engine?

Physics of Technology PHYS 1800