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Physics 1102 Introductory College Physics II Lectures: 5:45pm-7:25pm in Willey Hall 125 (there will be a 10minute break from 6:30-6:40pm) Instructor: J. Woods Halley (email: [email protected]) Course web page: http://www.physics.umn.edu/courses/2017/spring A few administrative clarifications: Permissions: If there are openings in a lab session to which you want to switch, go to the session and ask the TA if there is room. If there is, give him your name and he will contact me to help arrange the switch. Registration in the whole course is limited to 19 people per lab section because of available lab space. If registration drops below that level then new registrants can register on line. No permission numbers will be given for registration over the limit. Background from Introductory Physics I (1101) Newton's laws of motion and how to use them. What we will do in 1102: Properties of Solids and Liquids: Often Newton's laws apply, but new features arise when we consider the behavior of the atoms in these many atom systems leading to thermal physics and laws of thermodynamics Electricity and Magnetism: Providing new forces in Newtonian equations. Structure of Atoms: Newton doesn't work on very small scales. Conservation of energy and forms of energy: Let's consider a dropped ball. As I release it, its velocity is zero. As it gets to the floor, it's attained a finite velocity v. From what we know already, we can figure out the relationship between the height h from which it was dropped and the speed v, which it had when it hit the floor: distance fallen h = average speed x time=(1/2)vxtime (F=ma for a dropped ball.) v=time x g Therefore time =v/g. Put it in the 1st equation: h=(1/2)v(v/g) or gh=(1/2)v2 Kinetic and gravitational potential energy. From F=ma and the fact that the gravitational force is mg, we thus conclude that, for the dropped ball: gh=(1/2)v2 or multiplying both sides by m mgh=(1/2)mv2 at start just before it hits We say that the ball had Gravitational potential energy =mgh At the start of its fall and that energy changed form and became Kinetic energy = (1/2)mv2 Just before the ball hit the floor Thus for one isolated body, kinetic energy =1/2 mv2 + (gravitational) potential energy =mgh is conserved through free fall in the earth's gravitational field. Generalization: Kinetic plus potential energy for an isolated collection of interacting particles is conserved (as in a gas or liquid) . Potential Energy: Generally, a system which can evolve according to Newton's laws to have more kinetic energy is said to have initially had a form of potential energy. Examples: gravitational mgh elastic in springs ½ kx2 chemical I will show that elastic energy + kinetic energy is conserved for a mass m on a fixed spring with constant k: Consider two moments 1 and 2, close together in time, during the motion. F =-kx =ma=m(v2-v1)/(t2-t1) multiply by v≈(v2+v1)/2 and by t2-t1 write x≈(x2+x1)/2 and (t2-t1)v =x2-x1 Rearranging, you will find ½ mv12 +1/2 kx12 = ½ mv22 +1/2 kx22 Chemical Energy The forces between atoms don't always act like springs. But those forces do store potential energy which can be converted to kinetic energy. You may think of chemical energy as the potential energy stored in the bonds between the atoms of a system. Thermal Energy This is the part of the kinetic plus potential energy of a system of many atoms which does not arise from coherent motion of all the atoms. Picture a baseball in flight and a balloon on a string (not in flight). The atoms in the baseball are all moving in the same direction (coherent). The atoms in the balloon are all moving in different directions (incoherent). Δ contains coherent K parts of the velocities, as in the thrown baseball. ΔEth contains kinetic energy of the incoherent parts of the velocities, as in the air in the hot balloon. Summary for isolated systems: The change in the total energy ΔE = ΔK + ΔU+ ΔEth + ΔEchem =0 kinetic potential thermal chemical Example: A bomb lying motionless on the ground explodes. A person lifts her arm. There are many more but, often, systems aren't isolated. Energy Transfer between systems: One way is by the performance of work: example: lift a book throw a baseball games with carts The transfer of energy can be to or from any of the four forms we have mentioned. Energy Transfer between systems: One way is by the performance of work: example: lift a book throw a baseball games with carts The transfer of energy can be to or from any of the four forms we have mentioned. If work is performed on (or by) a system from the outside world then the previous relation becomes ΔE = ΔK + ΔU+ ΔEth + ΔEchem =W where W is the work done ON the system. In many applications of the conservation of energy, the system at hand (an engine, your body) does work on the external world (then W <0) . Consider lifting a book: The work done by my body on the book is mgh. It came from the chemical energy in my body. The work done by my body on the book is mgh. It came from the chemical energy in my body. Is it true that ΔEchem =W=-mgh for this process? a. yes, it's required by conservation of energy ΔEchem =W=+mgh b. no, because my arm warms up c. should be by the second law of d. no, yes,itit's required thermodynamics. The answer is b. Some of the chemical energy is converted to thermal energy. The second law of thermodynamics says that such processes never succeed in converting all the input energy into coherent motion associated with work. Thus the energy balance equation for lifting the book takes the form ΔEth + ΔEchem =-mgh with ΔEchem <0 and ΔEth>0 Efficiency: The efficiency for this booklifting exercise is defined as e = -W/ (-ΔEchem) The signs can be confusing: W is the work done ON the system (my body) so W<0 when I lift the book. The chemical energy in my body was depleted so ΔEchem <0 So e >0 and e will always be between 0 and 1 by the 2nd law of thermodynamics. Metabolism: Metabolism is the rate at which chemical energy is converted to coherent work (done by your muscles) and thermal energy in your body. Energy is stored in your body in the form of glucose which has the composition C6H12O6 meaning that the molecule consists of six carbon atoms, 12 hydrogen atoms and 6 oxygen atoms, bound together. In the process by which the chemical energy is released this molecule interacts with oxygen in your blood (which you got by breathing) as follows: C6H12O6 + O2 6CO2 +6H2O + energy Metabolism: Metabolism is the rate at which chemical energy is converted to coherent work (done by your muscles) and thermal energy in your body. Energy is stored in your body in the form of glucose which has the composition C6H12O6 meaning that the molecule consists of six carbon atoms, 12 hydrogen atoms and 6 oxygen atoms, bound together. In the process by which the chemical energy is released this molecule interacts with oxygen in your blood (which you got by breathing) as follows: C6H12O6 + O2 6CO2 +6H2O + energy Structure of glucose. Black is carbon atom, red is oxygen atom, blue hydrogen. Size is about 1 billionth of a meter. More generally, efficiency is e = work (energy associated with coherent motion) out thermal and chemical energy into system We usually consider what happens in 'steady state' when determining efficiencies. Then total outflow of energy per second equals total inflow (First law of thermodynamics). In the case of lifting a book, in steady state, the depletion of chemical energy will be replaced (when I eat and digest food) so -ΔEchem is the energy input. Generic diagram of energy flow in devices which output work from atomically incoherent sources (thermal energy and chemical energy) -- if system is red box (the 'engine') then using the definition of W in the work energy theorem, the work output is -W. Thermal engines. The energy input is all thermal, usually at a high temperature Th . The thermal energy output Qc is at a lower temperature Tc . The second law of thermodynamics say the we must have Qc >0 and e < 1. It is best to think of the diagram as representing energy flows in steady state and to replace Qc by Qc /t , Qc by Qc /t , and -W by power output P. An example is a car. Thermal energy is produced when the carbon in the gasoline is combined with the oxygen of the air via the reaction (combustion or burning) C + O2 CO2 + thermal energy to provide thermal energy input to the engine. The output work is used to push the car forward. If the fuel efficiency of your car is 35 miles per gallon how much energy is being provided to your engine for each mile you drive. (1.32 x 108 joules of thermal energy are available per gallon of gasoline.) A. 1.32 x 108 joules B. 3.77 x 106 joules C. 4.62 x 109 joules D. 2.03 x 106 joules If the fuel efficiency of your car is 35 miles per gallon how much energy is being provided to your engine for each mile you drive. (1.32 x 108 joules of thermal energy are available per gallon of gasoline.) A. 1.32 x 108 joules B. 3.77 x 106 joules C. 4.62 x 109 joules D. 2.03 x 106 joules Answer B. If the thermal efficiency of your car is 30% how much energy is being used to push the car forward per mile (if the gasoline is providing 3.77 x 106 joules of thermal energy per mile) A. 1.13 x 106 joules B. 2.64 x 106 joules C. 7.54 x 104 joules D. 3.96 x 107 joules Answer A. .30x 3.77 x 106 joules/mi= 1.13 x 106 joules/mi What force is the engine providing to drive the car forward in the last example (in Newtons). The energy provided in a mile was 1.13 x 106 joules (1 mile=1600 meters) A. 212 Newtons B. 1.81 x 109 Newtons C. 5.43 x 108Newtons D. 706 Newtons Answer D. Work = F x 1mile =1.13 x 106 joules F=1.13 x 106 joules/1600 meters = 706 Newtons What power, in horse power is the engine producing at 35mph in this car? (The force was 706 Newtons). 1 pound(lb)=4.4 newtons, 1 mile = 5280ft, 1 horsepower=550ft-lb/s A. 291 hp B. 15 hp C. 7 hp D. 0.4 hp Answer: C (706 Newtons x 35mph x 5280 ft/mi) /(3600 sec/hr x 4.4 N/lb x550 ft-lb/hp)=15hp A takehome message is that cars are overpowered. Now let's consider a bigger 'engine': the US energy economy. Look over at the right: The gray box says 'Rejected energy'. That's energy that wasn't used usefully by humans. The black box says 'Energy services'. That's energy that was useful for humans. Estimate the efficiency of the US energy economy. 54.64 A. 42% B. 73% C. 58% D. 136% 39.97 A This is somewhat misleading because a significant portion of the energy which was used was thermal energy (for heating buildings.) So far we briefly discussed these processes that change the form of energy: gravitational potential energy to KE (falling object, also hydropower) chemical energy to atomically coherent KE and PE plus thermal energy (humans) thermal energy to atomically coherent KE and PE plus thermal energy (engines) All these processes involve the performance of work. There is another way to transfer energy from one body to another without the performance of (atomically coherent) work.: Another way to transfer thermal energy to a body (not involving the performance of work) Transfer of thermal energy from another body at higher temperature. This is what happens in your house or apartment in the winter. Thermal energy is continuously transferred to the colder outside air through the walls and windows. Similarly from your body to the outside air when you go out. And many others... To analyse thermal energy transfers, we need a way to measure changes in thermal energy in a body. Here is a way to do it: Do an experiment in which work is done on the body by a force which is entirely frictional (no acceleration), while measuring the temperature of the body with a thermometer. The frictional force excites the atoms in the body and increases its thermal energy and the temperature rises. For small changes in temperature, the following relation holds as long as the body is not at its boiling or freezing temperature: work done = thermal energy added = constant x (change in temperature) work done = thermal energy added = constant x (change in temperature) Experimentally one finds that the constant depends on the material of which the body is made. is proportional to the mass of the body. Thus the quantity c = constant/mass is characteristic of the material of which the body is made. c is called the specific heat of the material That process tells you how to measure the specific heat (measure the work done, the mass and the change in temperature) and people have done it and tabulated the values of specific heats for many materials. Summary: The change Q in the thermal energy of a body with specific heat c and mass M undergoing a change ΔT is Q = McΔT Let's apply this to some situations in which thermal energy is transferred from one body (the initially higher temperature one) to another body (the initially lower temperature one) A can containing 500gm of water at 100 o C is put in contact with another can containing 1000 gm of water at 30 o C and the two touching cans are wrapped in insulation so that no thermal energy can escape. What is the final temperature of the water in the cans? (Ignore any thermal effects of the cans themselves) specific heat of water =4190 J/kgoC A. 86.7 C B. 76.7 C C. 53.3 C D. 65 C Answer C. The energy lost by the hot water is gained by the cold water (energy conservation). .5kgxCwater(100-T)= 1.0kgCwater(T-30) Solving for T: (1.5)T=0.5x100+30 T=80/1.5 C=53.3 C Note: In this case, the specific heat cancelled out, so it wasn't needed. The first problem in homework 1 is similar to this. Phase Changes The transfer of thermal energy from one body to another proceeds differently if the body is undergoing a PHASE CHANGE. Phase changes can be recognised experimentally by the occurrence of abrupt changes in properties. The most common examples are Melting (solid to or from liquid) Boiling (liquid to or from vapor) The thermal energy absorbed or released during a phase change is characterised by the HEAT OF TRANSFORMATION L of the material. ΔQ = ±ML where M is the amount of mass which has undergone the phase change and the sign is + if going from the low temperature phase to the high temperature phase (eg melting) - If going from the high temperature to the low temperature phase (eg freezing)