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AP Physics FLUIDS & THERMODYNAMICS Fluids Fluids are substances that can flow, such as liquids and gases, and even some solids We’ll just talk about the liquids & gases Review of Density (remember this from chem?) ρ = m/V ρ = density m = mass (kg) V = volume (m3) density units: kg/m3 Pressure P = F/A P = pressure (Pa) F = force (N) A = area (m2) Units for pressure: Pascals 1 Pa = 1 N/m2 Pressure is always applied as a normal force on a surface. Fluid pressure is exerted in all directions and is perpendicular to every surface at every location. Pressure Practice 1 Calculate the net force on an airplane window if cabin pressure is 90% of the pressure at sea level and the external pressure is only 50 % of the pressure at sea level. Assume the window is 0.43 m tall and 0.30 m wide. Atmospheric pressure Atmospheric pressure is normally about 100,000 Pascals. Differences in atmospheric pressure cause winds to blow Pressure of a Liquid The pressure of a liquid is sometimes called gauge pressure If the liquid is water, it is called hydrostatic pressure P = ρgh P = pressure (Pa) ρ = density (kg/m3) g = 9.81 m/s2 h = height of liquid column (m) Absolute Pressure Absolute pressure is 2. The depth of Lake obtained by adding Mead at the Hoover the atmospheric Dam is 600 ft. pressure to the What is the hydrostatic hydrostatic pressure pressure at the base of Patm + ρgh = Pabs the dam? What is the absolute pressure at the base of the dam? Buoyancy Force Floating is a type of equilibrium: An upward force counteracts the force of gravity for floating objects The upward force is called the buoyant force Archimedes’ Principle: a body immersed in a fluid is buoyed up by a force that is equal to the weight of the fluid it displaces Calculating Buoyant Force Fbuoy = ρVg Fbuoy: buoyant force exerted on a submerged or partially submerged object V: volume of displaced fluid ρ: density of displaced fluid When an object floats, the upward buoyant force equals the downward pull of gravity The buoyant force can float very heavy objects, and acts upon objects in the fluid whether they are floating, submerged, or even resting on the bottom Buoyant force on submerged objects A shark’s body is not Scuba divers use a neutrally buoyant, so a buoyancy control shark must swim system to maintain continuously or it will neutral buoyancy sink deeper (equilibrium) If the diver wants to rise, he inflates his vest, which increases his volume, or the water he displaces, and he accelerates upward Buoyant Force on Floating Objects If the object floats on the surface, we know that Fbuoy = Fg! The volume of displaced water equals the volume of the submerged portion of the object #3 Assume a wooden raft has 80.0 % of the density of water. The dimensions of the raft are 6.0 m long by 3.0 m wide by 0.10 m tall. How much of the raft rises above the level of the water when it floats? Buoyant Force Labs 1. Determine the density 2. Balloon Race: of water by using the Determine the buoyant force. buoyant force on your Equipment: balloon with the Beakers balloon, masses & a String balance Pulleys Without using the Weights/Masses balloon, design an Graduated cylinder apparatus so that (NO BALANCES!) when released, your balloon will hit the ceiling LAST. Moving Fluids When a fluid flows, The volume per unit mass is conserved time of a liquid flowing Provided there are no in a pipe is constant inlets or outlets in a throughout the pipe stream of flowing fluid, We can say this the same mass per unit because liquids are time must flow generally not everywhere in the compressible, so mass stream conservation is also volume conservation for a liquid Fluid Flow Continuity V = Avt Comparing two points V: volume of fluid (m3) in a pipe: A: cross sectional areas A1v1 = A2v2 at a point in the pipe A1, A2: cross sectional (m2) areas at points 1 and 2 v: the speed of fluid flow at a point in the v1, v2: speeds of fluid pipe (m/s) flow at points 1 and 2 t: time (s) Practice 4 & 5 4. A pipe of diameter 6.0 5. The water in a canal cm has fluid flowing flows 0.10 m/s where through it at 1.6 m/s. the canal is 12 meters How fast is the fluid deep and 10 meters flowing in an area of across. If the depth of the pipe in which the the canal is reduced diameter is 3.0 cm? to 6.5 m at an area How much water per where the canal second flows through narrows to 5.0 m, how the pipe? fast will the water be moving through the narrower region? Bernoulli’s Theorem The sum of the pressure, the potential energy per unit volume, and kinetic energy per unit volume at any one location in the fluid is equal to the sum of the pressure, the potential energy per unit volume, and the kinetic energy per unit volume at any other location in the fluid for a non-viscous incompressible fluid in streamline flow All other considerations being equal, when fluid moves faster, pressure drops Bernoulli’s Theorem P + ρgh + ½ ρv2 = constant 6. Knowing what you P = pressure (Pa) know about Bernoulli’s ρ = density of fluid (kg/m3) principle, design an g = grav. accel. constant airplane wing that (9.81 m/s2) you think will keep h = height above lowest an airplane aloft. point Draw a cross v = speed of fluid flow at a section of the wing. point in the pipe (m/s) Thermodynamics Thermodynamics is the Total Energy: study of heat and thermal energy E = U + K + Eint Thermal properties U = potential (heat & temperature) energy are based on the K = kinetic energy motion of individual molecules, so Eint= internal or thermodynamics thermal energy overlaps with chemistry Total Energy Potential and kinetic energies are specifically for “big” objects, and represent mechanical energy Thermal energy is related to the kinetic energy of the molecules of a substance Temperature & Heat Temperature is a measure of the average kinetic energy of the molecules of a substance. (like how fast the molecules are moving) The unit is °C or K. Temperature is NOT heat! Heat is the internal energy that is transferred between bodies in contact. The unit is Joules (J) or sometimes calories (cal) A difference in temperature will cause heat energy to be exchanged between bodies in contact. When two bodies are the same temp, they are in thermal equilibrium and no heat is transferred. Ideal Gas Law P: initial & final pressure (any unit) V: initial & final volume (any unit) T: initial & final temperature (K) T in Kelvins = T in °C + 273 #7 7. Suppose an ideal gas occupies 4.0 L at 23°C and 2.3 atm. What will be the volume of the gas if the temperature is lowered to 0°C and the pressure is increased to 3.1 atm? Ideal Gas Equation If you don’t remember this from chem, you shouldn’t have passed! P: pressure (Pa) V: volume (m3) n: number of moles R: gas law constant 8.31 J/(mol K) T: temp (K) 8 8. Determine the number of moles of an ideal gas that occupy 10.0 m3 at atmospheric pressure and 25°C. Ideal Gas Equation 9. Suppose a near vacuum contains 25,000 molecules of helium in one cubic P: pressure (Pa) meter at 0°C. What is V: volume (m3) the pressure? N: number of molecules kB: Boltzmann’s constant 1.38 x 10-23J/K T: temperature (K) Kinetic Theory of Gases 1. Gases consist of a large number of molecules that make elastic collisions with each other and the walls of their container 2. Molecules are separated, on average, by large distances and exert no forces on each other except when they collide 3. There is no preferred position for a molecule in the container, and no preferred direction for the velocity Average Kinetic Energy of a Gas Kave = 3/2 kBT Kave = average kinetic energy (J) kB = Boltzmann’s constant (1.38 x 10-23J/K) T = Temperature (K) The molecules have a range of kinetic energies, so we take the Kave 10 & 11 10. What is the average 11. Suppose nitrogen kinetic energy and and oxygen are in a average speed of sample of gas at oxygen molecules in a 100°C: gas sample at 0C°? a) What is the ratio of the average kinetic energies for the two molecules? b) What is the ratio of their average speeds? Thermodynamics The system boundary If the boundary is controls how the “closed to mass,” that environment affects means mass can’t get the system (for our in or out purposes, the system If the boundary is will almost always be “closed to energy,” an ideal gas) that means energy can’t get in or out What type of boundary does the earth have? First Law of Thermodynamics The work done on a system + the heat transferred to the system = the change in internal energy of the system. ΔU = W + Q ΔU = Eint = thermal energy (NOT potential energy – how stupid is that?) W = work done on the system (related to change in volume) Q = heat added to the system (J) – driven by temperature difference – Q flows from hot to cold First Law of Thermodynamics More about “U” U is the sum of the kinetic energies of all the molecules in a system (or gas) U = NKave U = N(3/2 kBT) U = n(3/2 RT) since kB = R/NA 12 & 13 12. A system absorbs 200 13. How much work does J of heat energy from the environment do on the environment and a system if its internal does 100 J of work on energy changes from the environment. 40,000 J to 45,000 J What is its change in without the addition of internal energy? heat? Gas Process The thermodynamic state of a gas is defined by pressure, volume, and temperature. A “gas process” describes how gas gets from one state to another state Processes depend on the behavior of the boundary and the environment more than they depend on the behavior of the gas Isothermal Process (Constant Temperature) Isobaric Process (Constant Pressure) Isometric Process (Constant Volume) Adiabatic Process (Insulated) Work Calculation of work done on a system (or by a system) is an important part of thermodynamic calculations Work depends upon volume change Work also depends upon the pressure at which the volume change occurs Work Done BY a gas Done ON a gas 14 & 15 14. Calculate the work 15. What is the change done by a gas that in volume of a cylinder expands from 0.020 m3 operating at to 0.80 m3 at constant atmospheric pressure if atmospheric pressure. its thermal energy How much work is done decreases by 230 J by the environment when 120 J of heat are when the gas expands removed from it? this much? Work (Isobaric) Work is Path Dependent 16 & 17 16. One mole of a gas 17. One mole of a gas goes from state A (200 goes from state A (200 kPa and 0.5 m3) to state kPa and 0.5 m3) to state B (150 kPa and 1.5 m3). B (150 kPa and 1.5 m3). What is the change in a. Draw this process temperature of the gas assuming the smoothest during this process? possible transition (straight line) b. Estimate the work done by the gas c. Estimate the work done by the environment Work Done by a Cycle When a gas undergoes a complete cycle, it starts and ends in the same state. the gas is identical before and after the cycle, so there is no identifiable change in the gas. ΔU = 0 for a complete cycle The environment, however, has been changed Work Done By Cycle Work done by the gas is equal to the area circumscribed by the cycle Work done by the gas is positive for clockwise cycles, and negative for counterclockwise cycles. Work done by the environment is opposite that of the gas 18 Consider the cycle ABCDA, where State A: 200 kPa, 1.0 m3 State B: 200 kPa, 1.5 m3 State C: 100 kPa, 1.5 m3 State D: 100 kPa, 1.0 m3 a. Sketch the cycle b. Graphically estimate the work done by the gas in one cycle c. Estimate the work done by the environment in one cycle 19 Calculate the heat necessary to change the temperature of one mole of an ideal gas from 600 K to 500 K a. At constant volume b. At constant pressure (assume 1 atm) Second Law of Thermodynamics No process is possible whose sole result is the complete conversion of heat from a hot reservoir into mechanical work (Kelvin-Planck statement) No process is possible whose sole result is the transfer of heat from a cooler to a hotter body (Clausius statement) Basically, heat can’t be completely converted into useful energy Heat Engines Heat engines can convert heat into useful work According to the 2nd Law of Thermodynamics, Heat engines always produce some waste heat Efficiency can be used to tell how much heat is needed to produce a given amount of work Heat Transfer Heat Engines Adiabatic vs. Isothermal Expansion Carnot Cycle Work and Heat Engines QH = W + QC QH: Heat that is put into the system and comes from the hot reservoir in the environment W: Work that is done by the system on the environment QC: Waste heat that is dumped into the cold reservoir in the environment 20 20. A piston absorbs 3600 J of heat and dumps 1500 J of heat during a complete cycle. How much work does it do during the cycle? Efficiency of Heat Engine In general, efficiency is related to what fraction of the energy put into a system is converted to useful work In the case of a heat engine, the energy that is put in is the heat that flows into the system from the hot reservoir Only some of the heat that flows in is converted to work. The rest is waste heat that is dumped into the cold reservoir Efficiency of Heat Engine Efficiency = W/QH = (QH – QC) / QH W: Work done by the engine on the environment QH: Heat absorbed from hot reservoir QC: Waste heat dumped into cold reservoir Efficiency is often given as percent efficiency YOUR TASK: find the efficiency of your hair dryer 21 A coal-fired stream plant is operating with 33% thermodynamic efficiency. If this is a 120 MW plant, at what rate is heat energy used? Carnot Engine Cycle Efficiency of Carnot Cycle For a Carnot engine, the efficiency can be calculated from the temperatures of the hot and cold reservoirs. Carnot Efficiency = (TH – TC) / TH TH: temperature of hot reservoir (K) TC: temperature of cold reservoir (K) 22 & 23 22. Calculate the Carnot 23. For #22, how much efficiency of a heat work is produced engine operating when 15 kJ of waste between the heat is generated? temperature of 60 and 1500°C. Entropy Entropy is disorder, or randomness The entropy of the universe is increasing. Ultimately, this will lead to what is affectionately known as “Heat Death of the Universe.” Entropy ΔS = Q/T ΔS: change in entropy (J/K) Q: heat going into the system (J) T: temperature (K) If change in entropy is positive, randomness or disorder has increased Spontaneous changes involve an increase in entropy Generally, entropy can go down only when energy is put into the system

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