RECAPCreate PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. novapdf.com) .Create PDF files without this message by purchasing novaPDF printer (http://www. com) .Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. com) .Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. com) .Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. Assumptions: There are many molecules moving in random directions at a variety of speeds. The molecules are. on average. Their separation >> their diameter. Collisions with other molecules or the container wall are perfectly elastic. And they interact only through collision. Time of collision << time between collisions. energy etc. not through attractive forces (PE). Molecules obey classical mechanics laws regarding collisions.com) .novapdf. far apart from each other. Create PDF files without this message by purchasing novaPDF printer (http://www. P). Equations: pV = nRT pV = nkT PV/T = const. T). Boyle’s Law (V.com) .novapdf. T). Charles’ Law (V. GayLussac’s Law (P. KE = 3/2 kT = ½ mv2 Vrms = 3kT/m Create PDF files without this message by purchasing novaPDF printer (http://www. Linear Expansion: Volume Expansion: You’re having trouble opening a glass jar. how can you make it easier? Create PDF files without this message by purchasing novaPDF printer (http://www.com) .novapdf. how can you make it easier? Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. Linear Expansion: Volume Expansion: You’re having trouble opening a glass jar.com) . com) .novapdf.AP Physics B Create PDF files without this message by purchasing novaPDF printer (http://www. pressure. volume… Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. Density.com) . Two systems are said to be in thermal equilibrium if there is no net flow of heat between them when they are brought into thermal contact.novapdf.com) . Create PDF files without this message by purchasing novaPDF printer (http://www. novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www. Two systems individually in thermal equilibrium with a third system are in thermal equilibrium with each other.com) . novapdf. Change in internal energy of a system is equal to the heat transferred to/from the system plus the work done on/by the system: ΔU = Q + W Comes from the law of conservation of energy. Create PDF files without this message by purchasing novaPDF printer (http://www. Sign convention: heat energy Q/W is positive when the system gains heat and negative when the system loses heat.com) . Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . The gas then applies a force on the piston wall pushing it a specific displacement. As you add heat. the temperature rises and thus the volume of the gas expands. Thus it can be said that a gas can do WORK.Suppose you had a piston filled with a specific amount of gas. com) .Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. 6 x 105 J.8 x 105 J of heat.com) . How much work have you done while walking? Create PDF files without this message by purchasing novaPDF printer (http://www.a) Jogging along the beach one day you do 4. What is the change in your internal energy? b) Switching over to walking.3 x 105 J of work and give off 3.2 x 105 J of heat and your internal energy decreases by 2.novapdf. you give off 1. com) . (b) The gas is then cooled at a constant volume until the pressure falls to 2.0 atm. (a) A gas is expanded from a volume of 1.0 atm Create PDF files without this message by purchasing novaPDF printer (http://www.Sketch a PV diagram and find the work done by the gas during the following stages.0 L at a constant pressure of 3.0 L to 3.novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www.0 atm from a volume of 3. d) The gas is then heated until its pressure increases from 2.0 atm to 3.com) .0 atm at a constant volume.c) The gas is then compressed at a constant pressure of 2.0 L.0 L to 1.novapdf. What is the NET WORK? Create PDF files without this message by purchasing novaPDF printer (http://www.com) .novapdf. com) .novapdf. not on the method by which the system arrives at a given state Quasi-static – a process that occurs slowly enough that a uniform pressure and temperature exist throughout all regions of the system at all times. Internal Energy is a function of state – it depends only on the state of a system. There is no friction nor dissipative Create PDF files without this message by purchasing novaPDF printer (http://www. To keep the temperature constant both the pressure and volume change to compensate. pressure goes down) “BOYLES’ LAW” Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . (Volume goes up. novapdf. The path of an isobaric process is a horizontal line called an isobar. ∆U = Q .com) .W can be used since the WORK is NEGATIVE in this case Create PDF files without this message by purchasing novaPDF printer (http://www.Heat is added to the gas which increases the Internal Energy (U) Work is done by the gas as it changes in volume. com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. com) .novapdf. NO HEAT can leave or enter the system. Create PDF files without this message by purchasing novaPDF printer (http://www.(GREEKadiabatos"impassable") In other words.ADIABATIC. novapdf.com) .Create PDF files without this message by purchasing novaPDF printer (http://www. Create PDF files without this message by purchasing novaPDF printer (http://www. Example A gas expands from an initial volume of 0.com) .62 m3 as the pressure increases linearly from 110 kPa to 230 kPa. Find the work done by the gas.novapdf.40 m3 to a final volume of 0. work must be done.novapdf. For the reverse to happen. Example? Create PDF files without this message by purchasing novaPDF printer (http://www. Heat will only flow spontaneously from a body of higher temperature to a body of lower temperature.com) . Create PDF files without this message by purchasing novaPDF printer (http://www.com) . Disorder in the universe can only increase.novapdf. Heat flows from a HOT reservoir to a COLD reservoir QH = remove from.novapdf.com) . absorbs = hot QC= exhausts to. expels = cold Create PDF files without this message by purchasing novaPDF printer (http://www. novapdf.Qout Qin Qin Create PDF files without this message by purchasing novaPDF printer (http://www.com) . = Wout = 1 .In order to determine the thermal efficiency of an engine you have to look at how much ENERGY you get OUT vs how much you energy you take IN. Eff. 0% performs 1250 J of work.A heat engine with an efficiency of 24. Find (a) the heat absorbed from the hot reservoir. and (b) the heat given off to the cold reservoir.novapdf.com) . Create PDF files without this message by purchasing novaPDF printer (http://www. The RATE at which WORK is DONE Create PDF files without this message by purchasing novaPDF printer (http://www. For example: The RATE at which heat is absorbed! The RATE at which heat is expelled.novapdf.Sometimes it is useful to express the energy usage of an engine as a RATE.com) QH t QC t W POWER t . Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . not long after steam engines had become efficient enough to begin replacing water wheels.com) . Not surprisingly. Carnot visualized the heat engine as a kind of water wheel in which heat (the “fluid”) dropped from a high temperature to a low temperature.Our goal is to figure out just how efficient such a heat engine can be: what’s the most work we can possibly get for a given amount of fuel? The efficiency question was first posed—and solved—by Sadi Carnot in 1820.novapdf. just like a water wheel. losing “potential energy” which the engine turned into work done. perhaps. Create PDF files without this message by purchasing novaPDF printer (http://www. at that time the main power sources for industry. and be 50% efficient.novapdf. Therefore. Picture a water wheel that takes in water at the top of a waterfall. the fluid would give up all its heat energy. So. Create PDF files without this message by purchasing novaPDF printer (http://www. but lets it out halfway down. the efficiency of an ideal engine operating between two temperatures will be equal to the fraction of the temperature drop towards absolute zero that the heat undergoes. = TH – TC TH . and an engine taking in heat at T and shedding it at ½T will be utilizing half the possible heat. it will give up half its heat. if it falls only half way to absolute zero from its beginning temperature. from which he figured out that on being cooled to absolute zero.com) Carnot Eff.Carnot a believed that there was an absolute zero of temperature. novapdf.com) .Carnot temperatures must be expressed in KELVIN!!!!!! The Carnot model has 4 parts •An Isothermal Expansion •An Adiabatic Expansion •An Isothermal Compression •An Adiabatic Compression The PV diagram in a way shows us that the ratio of the heats are symbolic to the ratio of the 2 temperatures Create PDF files without this message by purchasing novaPDF printer (http://www. and its cold reservoir is at a temperature of 295 K.novapdf.com) . what is the temperature of the hot reservoir? Create PDF files without this message by purchasing novaPDF printer (http://www.If the heat engine from the example before is operating at a maximum efficiency. A particular engine has a power output of 5000 W and an efficiency of 25%. If the engine expels 8000 J of heat in each cycle, find (a) the heat absorbed in each cycle and (b) the time for each cycle Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) The efficiency of a Carnot engine is 30%. The engine absorbs 800 J of heat per cycle from a hot temperature reservoir at 500 K. Determine (a) the heat expelled per cycle and (b) the temperature of the cold reservoir Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) Q T C The relationship for a Carnot engine, C can be rearranged to Q H TH QC QH TC TH . The quantity Q/T is the change in entropy, ΔS: Q ΔS T R The temperature, again, must be in Kelvins, the subscript R refers to reversible process. Units for entropy = J/K Entropy is a function of state (like internal energy) – only the state of the system determines the entropy Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) 125 kg chunk of ice melt at 0ºC.Calculate the change in entropy when a 0. Assume the melting occurs reversibly. Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . ) Irreversible processes increase the entropy of the universe. but if so. ΔS > 0 Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . (The entropy of one part of the universe may change. The entropy of a Carnot Engine: as the engine operates. the entropy of the hot reservoir decreases. since heat QH leaves. ΔS = 0 for a Carnot Engine. the change in the entropy of the hot reservoir is QH ΔS H TH (minus indicates decrease in S) the change in the entropy of the cold reservoir is QC ΔS C TC Thus. the entropy of another part must change in the opposite way by the same amount. the total change in entropy is QC QH QC Q H (equals zero because ) ΔS C S H 0 TC TH TC TH Thus. This is also true for any reversible process: the total entropy of the universe does not change Reversible processes do not change the total entropy of the universe. Find the change in entropy of the universe.com) .A hot reservoir at the temperature 576 K transfers 1050 J of heat irreversibly to a cold reservoir at the temperature 305 K.novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www. The Second Law of Thermodynamics in terms of Entropy: The total entropy of the universe does not change when a reversible process occurs and increases when an irreversible process occurs. Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . com) .AP Physics B Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www. a fluid is a substance that has no fixed shape and yields easily to external pressure.com) .novapdf.By definition. Typically. Create PDF files without this message by purchasing novaPDF printer (http://www. That is once you place a liquid in a sealed container you can DO WORK on the FLUID as if it were an object.novapdf. The PRESSURE you apply is transmitted throughout the liquid and over the entire length of the fluid itself.com) . liquids are considered to be incompressible. Pressure always acts perpendicular to the surface.Can exert pressure in any direction.novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www.com) . com) .Pat is a direct result of the weight of the air above us. Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. Suppose a Fluid (such as a liquid) is at REST. This is because pressure is greatly affected by the DEPTH of the object. Since the bottom of each object is deeper than the top the pressure is greater at the bottom. we call this HYDROSTATIC PRESSURE. Notice that the arrows on TOP of the objects are smaller than at the BOTTOM.novapdf.com) . Create PDF files without this message by purchasing novaPDF printer (http://www. novapdf. If we were to draw an FBD for this object we would have three forces Create PDF files without this message by purchasing novaPDF printer (http://www.com) .Suppose we had an object submerged in water with the top part touching the atmosphere. which is a CONSTANT. pressure is force per unit area.novapdf. Note: The initial pressure in this case is atmospheric pressure.But recall.com) . Po=1x105 N/m2 FINAL EQUATION: DP = rgh Create PDF files without this message by purchasing novaPDF printer (http://www. Assume that the density of water is 1000 kg/m3 and that Po= 1.01 x 105 Pa (N/m2). b) Calculate the total force exerted on the outside of a 30. Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.0 cm diameter circular submarine window at this depth.a) Calculate the absolute pressure at an ocean depth of 1000 m.com) . novapdf.Therefore: PA = PB = PC = PD (because they all have the same depth) Create PDF files without this message by purchasing novaPDF printer (http://www.com) . novapdf.com) . Mercury Barometer: measures atmospheric pressure Open Tube Manometer: measures pressure in a container Po = 0 P = Patm Patm = 0 + ρgh Patm = ρgh P = Patm + ρgh Example: blood pressure cuff Create PDF files without this message by purchasing novaPDF printer (http://www. The idea behind this is called PASCAL’S PRINCIPLE Create PDF files without this message by purchasing novaPDF printer (http://www. the PRESSURE is the same everywhere. You can take advantage of the fact that the pressure is the same in a closed system as it has MANY applications.com) . on the other hand MAY or MAY NOT equal the initial force applied. The force. It depends on the AREA. if you apply a force at one part of the system the pressure is the same at the other end of the system. Since this is true.novapdf.If you take a liquid and place it in a system that is CLOSED like plumbing for example or a car’s brake line. Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . novapdf.com) .Create PDF files without this message by purchasing novaPDF printer (http://www. novapdf. it is raised with a hydraulic lift. and the radius of the large piston is 17cm. If the radius of the small piston is 4.com) . find the force that must be exerted on the small piston to lift the car.To inspect a 14.000 N car.0 cm. Create PDF files without this message by purchasing novaPDF printer (http://www. it is buoyed upwards by a force called the buoyant force.When an object is immersed in a fluid.novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www.com) . such as a liquid. If you were to weight the water displaced it also would weigh 3 lbs. Create PDF files without this message by purchasing novaPDF printer (http://www." In the figure.com) . This is the buoyant force that acts upward to cancel out part of the force. we see that the difference between the weight in AIR and the weight in WATER is 3 lbs.novapdf." An object is buoyed up by a force equal to the weight of the fluid displaced. novapdf.com) .*V = A(h2 – h1) Create PDF files without this message by purchasing novaPDF printer (http://www. A bargain hunter purchases a "gold" crown at a flea market. After she gets home, she hangs it from a scale and finds its weight in air to be 7.84 N. She then weighs the crown while it is immersed in water (density of water is 1000 kg/m3) and now the scale reads 6.86 N. Is the crown made of pure gold if the density of gold is 19.3 x 103 kg/m3? Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) A piece of wood with a density o 706 kg/m3 is tied with a string to the bottom of a water-filled flask. The wood is completely immersed, and has a volume of 8.00 x 10-6 m3. What is the tension in the string? Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) Steady – velocity of the fluid particles at any point is constant as time passes Unsteady – velocity at a point in the fluid changes as time passes (ex: Turbulent flow: extremely unsteady flow) Incompressible – density of the fluid remains constant as pressure changes (usually liquids) Compressible – density of the fluid changes as pressure changes (usually gases) Viscous – “a large viscosity” – doesn’t readily flow: the viscosity hinders the neighboring layers of fluid from sliding past each other. Nonviscous – “a low viscosity” – flows readily – layers are not hindered from sliding past each other. Rotational – a part of the fluid has rotational as well as translational motion. Place a paddle wheel in the fluid, if it rotates, flow is rotational. Irrotational – fluid has only translational motion. The paddle wheel will not turn. Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) com) .novapdf.Create PDF files without this message by purchasing novaPDF printer (http://www. Consider a pipe with a fluid moving within it. A L v Mass flow rate is: m = Vr = ALr = Avr Dt Dt Dt A v (m = rV) L Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . v2 A2 Using the Mass Flow rate equation and the idea that a certain mass of water is constant as it moves to a new pipe section: We have the Fluid Flow Continuity equation Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. The MASS that flows into a region = The MASS that flows out of a region.v1 A 1 L2=v2t L1=v1t The first thing you MUST understand is that MASS is NOT CREATED OR DESTROYED! IT IS CONSERVED.com) . ) Create PDF files without this message by purchasing novaPDF printer (http://www.0 cm. If the capillaries have a total cross sectional area of 3000 cm2.novapdf. what is the speed of the blood in them? (Equation of continuity – the last equation we derived last class.The speed of blood in the aorta is 50 cm/s and this vessel has a radius of 1.com) . com) .novapdf.What happens to the roof of the “wind tunnel”? Create PDF files without this message by purchasing novaPDF printer (http://www. com) . He especially wanted to incorporate pressure into his idea as well.The Swiss Physicist Daniel Bernoulli. Conceptually. was interested in how the velocity changes as the fluid moves through a pipe of different area. his principle is stated as: "an increase in velocity of a stream of fluid results in a decrease of pressure in the fluid” Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. Steady flow.Assumptions: Laminar flow.com) .novapdf. Incompressible fluid. Create PDF files without this message by purchasing novaPDF printer (http://www. According to Newton’s 3rd law.novapdf. Create PDF files without this message by purchasing novaPDF printer (http://www.com) . the second section of water applies an equal and opposite force back on the first. Pressure*Area is substituted for Force.X=L F1 on 2 -F2 on 1 Work is done by a section of water applying a force on a second section in front of it over a displacement. Thus is does negative work as the water still moves FORWARD. novapdf. The fluid in section 1 flows towards section 2 a distance L1 and in doing so pushes the fluid in section 2 a distance L2. So the work is NEGATIVE. Create PDF files without this message by purchasing novaPDF printer (http://www. As the water moves UP the force due to gravity is DOWN.com) .v2 A2 y2 L1=v1t L2=v2t v1 y1 A1 ground Work is also done by GRAVITY as the water travels a vertical displacement UPWARD. novapdf. and work is done.The fluid in the first section is pushed by the fluid to the left of it. W1 = F1L1 = P1A1L1 (Since P = F/A) Create PDF files without this message by purchasing novaPDF printer (http://www.com) . W1 = F1L1 = P1A1L1 (Since P = F/A) The fluid in the second section is held back by the fluid to the right of it.com) .The fluid in the first section is pushed by the fluid to the left of it. and negative work is done. W2 = -F2L2 = -P2A2L2 Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. and work is done. W2 = -F2L2 = -P2A2L2 And negative work is also done by gravity. and work is done.com) . W1 = F1L1 = P1A1L1 (Since P = F/A) The fluid in the second section is held back by the fluid to the right of it.novapdf.The fluid in the first section is pushed by the fluid to the left of it. and negative work is done. resisting the motion: W3 = -mg (y2 – y1) Create PDF files without this message by purchasing novaPDF printer (http://www. Total work done: W = W1 + W2 + W3 Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf.com) . com) .P2A2L2 . so: ½ mv22 – ½ mv12 = P1A1L1 .novapdf.Total work done: W = W1 + W2 + W3 And this work is equal to the change in kinetic energy of the system.mgy2 + mgy1 Create PDF files without this message by purchasing novaPDF printer (http://www. P2A2L2 . so: ½ mv22 – ½ mv12 = P1A1L1 .Total work done: W = W1 + W2 + W3 And this work is equal to the change in kinetic energy of the system.com) .novapdf.mgy2 + mgy1 Realize that m = rV = rAL Create PDF files without this message by purchasing novaPDF printer (http://www. so: ½ mv22 – ½ mv12 = P1A1L1 .Total work done: W = W1 + W2 + W3 And this work is equal to the change in kinetic energy of the system. using the fact that A1L1 = A2L2 to get: ½rv22 – ½ rv12 = P1 – P2 – rgy2 + rgy1 Create PDF files without this message by purchasing novaPDF printer (http://www.com) .P2A2L2 .novapdf.mgy2 + mgy1 Realize that m = rV = rAL Plug this value of m in and cancel the AL in each term. novapdf.½rv22 – ½ rv12 = P1 – P2 – rgy2 + rgy1 Rearrange to get: P1 + ½ rv12 + rgy1 = P2 + ½rv22 + rgy2 Create PDF files without this message by purchasing novaPDF printer (http://www.com) . ½rv22 – ½ rv12 = P1 – P2 – rgy2 + rgy1 Rearrange to get: P1 + ½ rv12 + rgy1 = P2 + ½rv22 + rgy2 Or more simply: P + ½ rv2 + rgy = const. Create PDF files without this message by purchasing novaPDF printer (http://www. this becomes the hydrostatic equation.novapdf. if v = 0. Notice.com) . com) .6 cm-diameter pipe on the second floor 5. If the water is pumped at a speed of 0.0 m above? Create PDF files without this message by purchasing novaPDF printer (http://www.novapdf. what will be the flow speed and pressure in a 2.0 cm diameter pipe in the basement under a pressure of 3.Water circulates throughout the house in a hot-water heating system.50 m/s through a 4.0 atm.